20Cxx Representation theory of groups
This subtopic studies representation theory of groups, where groups are analyzed through linear actions on vector spaces and modules.
Specific topics
20C05 Group rings of finite groups and their modules
Overview
20C05 studies group rings of finite groups and their modules in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for group rings of finite groups and their modules
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C07 Group rings of infinite groups and their modules
Overview
20C07 studies group rings of infinite groups and their modules in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for group rings of infinite groups and their modules
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C08 Hecke algebras and their representations
Overview
20C08 studies hecke algebras and their representations in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for hecke algebras and their representations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C10 Integral representations of finite groups
Overview
20C10 studies integral representations of finite groups in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integral representations of finite groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C11 $p$-adic representations of finite groups
Overview
20C11 studies $p$-adic representations of finite groups in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for $p$-adic representations of finite groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C12 Integral representations of infinite groups
Overview
20C12 studies integral representations of infinite groups in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integral representations of infinite groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C15 Ordinary representations and characters
Overview
20C15 studies ordinary representations and characters in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for ordinary representations and characters
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C20 Modular representations and characters
Overview
20C20 studies modular representations and characters in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for modular representations and characters
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C25 Projective representations and multipliers
Overview
20C25 studies projective representations and multipliers in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for projective representations and multipliers
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C30 Representations of finite symmetric groups
Overview
20C30 studies representations of finite symmetric groups in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of finite symmetric groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C32 Representations of infinite symmetric groups
Overview
20C32 studies representations of infinite symmetric groups in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of infinite symmetric groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C33 Representations of finite groups of Lie type
Overview
20C33 studies representations of finite groups of lie type in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of finite groups of lie type
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C34 Representations of sporadic groups
Overview
20C34 studies representations of sporadic groups in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representations of sporadic groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C35 Applications of group representations to physics
Overview
20C35 studies applications of group representations to physics in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for applications of group representations to physics
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks
20C40 Computational methods (group representations)
Overview
20C40 studies computational methods (group representations) in representation theory of groups. It studies modules, characters, and realizations of groups via linear transformations.
Related Wikipedia Page
Representation Theory Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for computational methods (group representations)
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze symmetry, compute characters, and study modules over group algebras.
Applications
- Characters and modules
- Integral and modular representations
- Computational representation theory
References
Recommended Textbooks