Chris Berg ; Monica Vazirani
-
(ℓ,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
(ℓ,0)-Carter Partitions and their crystal theoretic interpretation Conference paper
Authors: Chris Berg 1; Monica Vazirani 1
NULL##NULL
Chris Berg;Monica Vazirani
1 Department of Mathematics [Univ California Davis]
In this paper we give an alternate combinatorial description of the "(ℓ,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 (ℓ,0)-Carter partition is fundamentally related to the hook lengths of the partition. The representation-theoretic significance of their combinatoric on an ℓ-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 ^slℓ, whose nodes are labeled by ℓ-regular partitions. Here we give a fairly simple crystal-theoretic rule which generates all (ℓ,0)-Carter partitions in the graph of B(Λ0).
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