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Stephen Lewis ; Nathaniel Thiem - Nonzero coefficients in restrictions and tensor products of supercharacters of Un(q) (extended abstract)

dmtcs:2840 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2840
Nonzero coefficients in restrictions and tensor products of supercharacters of Un(q) (extended abstract)Conference paper

Authors: Stephen Lewis 1; Nathaniel Thiem 2

  • 1 Department of Mathematics [Seattle]
  • 2 Department of Mathematics, University of Colorado

The standard supercharacter theory of the finite unipotent upper-triangular matrices Un(q) gives rise to a beautiful combinatorics based on set partitions. As with the representation theory of the symmetric group, embeddings of Um(q)Un(q) for mn lead to branching rules. Diaconis and Isaacs established that the restriction of a supercharacter of Un(q) is a nonnegative integer linear combination of supercharacters of Um(q) (in fact, it is polynomial in q). In a first step towards understanding the combinatorics of coefficients in the branching rules of the supercharacters of Un(q), this paper characterizes when a given coefficient is nonzero in the restriction of a supercharacter and the tensor product of two supercharacters. These conditions are given uniformly in terms of complete matchings in bipartite graphs.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: supercharacters,set-partitions,matching,bipartite graphs,unipotent upper-triangular matrices,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • FRG: Collaborative Research: Characters, Liftings, and Types: Investigations in p-adic Representation Theory; Funder: National Science Foundation; Code: 0854893

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