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

By Xavier Yvonne. 2005

49 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ccc2906f1f0b8ffd55e66974fe3c35df6ad9c132

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In Algebra and Number Theory

  1. E. Vasserot
  2. Raphaël Rouquier
  3. M. Varagnolo
  4. P. Shan
  5. Ben Webster
  6. H. Nakajima
  7. Alexander S. Kleshchev
  8. Masaki Kashiwara

In Discrete Mathematics and Combinatorics

  1. E. Vasserot
  2. P. Shan
  3. M. Varagnolo
  4. Raphaël Rouquier
  5. Alexander S. Kleshchev
  6. Aaron D. Lauda
  7. Jonathan Brundan
  8. David E. V. Rose

In Geometry and Topology

  1. E. Vasserot
  2. M. Varagnolo
  3. Ben Webster
  4. Alexander S. Kleshchev
  5. P. Shan
  6. Raphaël Rouquier
  7. H. Nakajima
  8. Aaron D. Lauda

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