Deformations of Weyl's Denominator Formula

Abstract

We introduce a series of conjectured identities that deform Weyl's denominator formula and generalize Tokuyama's formula to other root systems. These conjectures generalize a number of well-known results due to Okada. We also prove a related result for $B'_n$ that generalizes a theorem of Simpson.

Keywords

• lattice paths
• alternating sign matrices
• weyl's denominator formula
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]