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

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

2005-05-18

arxiv.org/abs/math/0505379v3

Mathematics

Representation Theory

This is the final version (published version). No new result since Version 2, but major changes of the organization of the pap

Scientific paper

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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