Towards multiplicities for categories O of cyclotomic rational Cherednik algebras

Abstract

Varagnolo and Vasserot conjectured an equivalence between the category O for a cyclotomic Rational Cherednik algebra and a truncation of an affine parabolic category O of type A. In this paper we reduce their conjecture to some purely combinatorial conjecture. Our principal tool for the reduction is the theory of categorical sl_2-actions on highest weight categories. Then we prove our combinatorial conjecture in some cases.

This paper has been withdrawn by the author. 25 pages; v2, 36 pages, substantial changes, more material added, replaced by arXiv:1305.4894

References in corpus (5)

• 2-Kac-Moody algebras
• Quiver Schur algebras and q-Fock space
• On category O for cyclotomic rational Cherednik algebras
• Highest weight sl_2-categorifications I: crystals
• Highest weight sl_2-categorifications II: structure theory

Cited by in corpus (1)

• On representations of rational Cherednik algebras in complex rank