Arc spaces and DAHA representations

Abstract

A theorem of Y. Berest, P. Etingof and V. Ginzburg states that finite dimensional irreducible representations of a type A rational Cherednik algebra are classified by one rational number m/n. Every such representation is a representation of the symmetric group S_n. We compare certain multiplicity spaces in its decomposition into irreducible representations of S_n with the spaces of differential forms on a zero-dimensional moduli space associated with the plane curve singularity x^m=y^n.

16 pages

References in corpus (3)

• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• Lecture notes on Cherednik algebras
• Towards a Global Springer Theory II: the double affine action

Cited by in corpus (2)

• Introduction to Khovanov Homologies. III. A new and simple tensor-algebra construction of Khovanov-Rozansky invariants
• A new Plethystic Symmetric Function Operator and The rational Compositional Shuffle Conjecture at t=1/q