An algorithm for computing the canonical bases of higher-level q-deformed Fock spaces
We derive a straightening-free algorithm that computes the canonical bases of any higher-level q-deformed Fock space.
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arXiv subjects
Xavier Yvonne
Publications and source records attributed to Xavier Yvonne.
Canonical bases of higher-level q-deformed Fock spaces
We show that the transition matrices between the standard and the canonical bases of infinitely many weight subspaces of the higher-level q-deformed Fock spaces are equal.
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A conjecture for q-decomposition matrices of cyclotomic v-Schur algebras
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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