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A conjecture for q-decomposition matrices of cyclotomic v-Schur algebras

Xavier Yvonne
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Abstract

The Jantzen sum formula for cyclotomic v-Schur algebras yields an identity for some q-analogues of the decomposition matrices of these algebras. We prove a similar identity for matrices of canonical bases of higher-level Fock spaces. We conjecture then that those matrices are actually identical for a suitable choice of parameters. In particular, we conjecture that decomposition matrices of cyclotomic v-Schur algebras are obtained by specializing at q=1 some transition matrices between the standard basis and the canonical basis of a Fock space.

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BibTeXRIS

Xavier Yvonne. 2006-04-27. A conjecture for q-decomposition matrices of cyclotomic v-Schur algebras. https://arxiv.org/abs/math/0505379

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