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

Xavier Yvonne (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Mots clés: Decomposition matrices; cyclotomic Schur algebras; canonical bases; Fock spaces

Domaines: Théorie des représentations [math.RT]

Xavier Yvonne. A conjecture for q-decomposition matrices of cyclotomic v-Schur algebras. 2005. ⟨hal-00004920v1⟩