30 citations · 416 across the 73 of their papers we have counts for
19 papers · 1 filter
A weight-formula for all highest weight modules, and a higher order parabolic category
Apoorva Khare, G. Krishna Teja
Let be a complex Kac-Moody algebra, with Cartan subalgebra . Also fix a weight . For an arbitrary highes…
From Cauchy's determinant formula to bosonic and fermionic immanant identities
Apoorva Khare, Siddhartha Sahi
Cauchy's determinant formula (1841) involving is a fundamental result in symmetric function theory. It has been extended in several directions, including…
The Weyl-Kac weight formula
Gurbir Dhillon, Apoorva Khare
We provide the first formulae for the weights of all simple highest weight modules over Kac-Moody algebras. For generic highest weights, we present a formula for the weights of sim…
Faces of highest weight modules and the universal Weyl polyhedron
Gurbir Dhillon, Apoorva Khare
Let be a highest weight module over a Kac-Moody algebra , and let conv denote the convex hull of its weights. We determine the combinatorial isomorphism type…
The weights of simple modules in Category for Kac-Moody algebras
Gurbir Dhillon, Apoorva Khare
We give the first positive formulas for the weights of every simple highest weight module over an arbitrary Kac-Moody algebra. Under a mild condition on the highest weight,…
On Category over triangular Generalized Weyl Algebras
Apoorva Khare, Akaki Tikaradze
We analyze the BGG Category over a large class of generalized Weyl algebras (henceforth termed GWAs). Given such a "triangular" GWA for which Category d…