We consider the construction of refined Chern–Simons torus knot invariants by M. Aganagic
and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's …

Let $ R $ be the complete local ring of a complex plane curve germ and $ S $ its
normalization. We propose a conjecture relating the virtual weight polynomials of the Hilbert …

This chapter gives an expository account of some unexpected connections which have
arisen over the last few years between Macdonald polynomials, invariants of torus knots …

Our main result is a generalization, to all affine Weyl groups, of P. Johnson's proof of D.
Armstrong's conjecture for the expected number of boxes in a simultaneous core. This …

Motivated by the study of simultaneous cores, we give three proofs (in varying levels of
generality) that the expected norm of a weight in a highest weight representation V λ of a …

The k-Schur functions are a generalization of Schur functions originally studied by Lapointe
and Morse, arising as the cohomology of the affine Grassmannian. These functions are thus …

We prove that the expected norm of a weight in a highest weight representation g (λ) of a
complex simple Lie algebra g is 1 h+1 (λ, λ+ 2ρ) by relating it to the “Winnie-the-Pooh …