Abstract
Cosets, Restricted and Induced Representations describes cosets, a basic concept from group theory, and uses cosets to produce representations of a group given a representation of a subgroup.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A collection of non-empty disjoint subsets of a set S whose union is S is called a partition of S. This is a set partition, as opposed to the integer partitions encountered previously. Any equivalence relation on a set partitions the set into equivalence classes. Note the use of the word “partition” as both a noun and a verb.
- 2.
If X ⊂ Y , then the inclusion mapping i : X↪Y is defined as i(x) = x for all x ∈ X.
- 3.
Because \(f \in \mathcal {F}\) and H = G.
References
Sagan, B. E. (1991). The symmetric group; representations, combinatorial algorithms, and symmetric functions (2nd ed.). New York, Berlin, Heidelberg, Barcelona, Hong Kong, London, Paris, Singapore, Tokyo: Springer.
Sternberg, S. (1994). Group Theory and Physics. Cambridge, New York, Melbourne: Cambridge University Press.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Howe, R.M. (2022). Cosets, Restricted and Induced Representations. In: An Invitation to Representation Theory. Springer Undergraduate Mathematics Series(). Springer, Cham. https://doi.org/10.1007/978-3-030-98025-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-98025-2_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-98024-5
Online ISBN: 978-3-030-98025-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)