arXiv subjects

Igor Makhlin

Publications and source records attributed to Igor Makhlin.

20 records · Page 2Linked to original sources

arXiv2016

A Combinatorial Formula for Affine Hall-Littlewood Functions via a Weighted Brion Theorem

We present a new combinatorial formula for Hall-Littlewood functions associated with the affine root system of type $\tilde A_{n-1}$, i.e. corresponding to the affine Lie algebra $\hat{\mathfrak{sl}}_n$. Our formula has the form of a sum over the elements of a basis constructed by Feigin, Jimbo, Loktev, Miwa and Mukhin in the corresponding irreducible representation. Our formula can be viewed as a weighted sum of exponentials of integer points in a certain infinite-dimensional convex polyhedron. We derive a weighted version of Brion's theorem and then apply it to our polyhedron to prove the formula.

math.CO↗

arXiv2014

Characters of Feigin-Stoyanovsky subspaces and Brion's theorem

We give an alternative proof of the main result of the paper http://arxiv.org/abs/math/0112104, the proof relies on Brion's theorem about convex polyhedra. The result itself can be viewed as a formula for the character of the Feigin-Stoyanovsky subspace of an integrable irreducible representation of the affine Lie algebra $\widehat{\mathfrak{sl}_n}(\mathbb{C})$. Our approach is to assign integer points of a certain polytope to the vectors comprising a monomial basis of the subspace and then compute the character via (a variation of) Brion's theorem.

math.RT↗