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Chris Berg ; Monica Vazirani - (,0)-Carter Partitions and their crystal theoretic interpretation

dmtcs:3650 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3650
(,0)-Carter Partitions and their crystal theoretic interpretation Conference paper

Authors: Chris Berg 1; Monica Vazirani 1

  • 1 Department of Mathematics [Univ California Davis]

In this paper we give an alternate combinatorial description of the "(,0)-Carter partitions''. Our main theorem is the equivalence of our combinatoric and the one introduced by James and Mathas (A q-analogue of the Jantzen-Schaper theorem). The condition of being an (,0)-Carter partition is fundamentally related to the hook lengths of the partition. The representation-theoretic significance of their combinatoric on an -regular partition is that it indicates the irreducibility of the corresponding Specht module over the finite Hecke algebra. We use our result to find a generating series which counts the number of such partitions, with respect to the statistic of a partition's first part. We then apply our description of these partitions to the crystal graph B(Λ0) of the basic representation of ^sl, whose nodes are labeled by -regular partitions. Here we give a fairly simple crystal-theoretic rule which generates all (,0)-Carter partitions in the graph of B(Λ0).


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: Representation theory,Hecke algebras,Combinatorics of Young tableaux,Crystals of affine Lie algebras,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Vertical Integration of Research and Education in the Mathematical Sciences - VIGRE: Research Focus Groups in Mathematics; Funder: National Science Foundation; Code: 0135345
  • Irreducible Representations of the Affine and Double Affine Hecke Algebras of Type A; Funder: National Science Foundation; Code: 0301320

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