Abstract
We present a new combinatorial formula for Hall–Littlewood functions associated with the affine root system of type A~ n - 1, i.e., corresponding to the affine Lie algebra 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.
Original language | English |
---|---|
Pages (from-to) | 1703-1747 |
Number of pages | 45 |
Journal | Selecta Mathematica, New Series |
Volume | 22 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jul 2016 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics
- General Physics and Astronomy