1,496 research outputs found
Intertwining operators between line bundles on Grassmannians
Let G=GL(n,F) where F is a local field of arbitrary characteristic, and let
be representations induced from characters of two maximal
parabolic subgroups . We explicitly determine the space
of intertwining operators and prove that it has dimension
at most 1 in all cases.Comment: 7 page
Some remarks on non-symmetric interpolation Macdonald polynomials
We provide elementary identities relating the three known types of
non-symmetric interpolation Macdonald polynomials. In addition we derive a
duality for non-symmetric interpolation Macdonald polynomials. We consider some
applications of these results, in particular for binomial formulas involving
non-symmetric interpolation Macdonald polynomials.Comment: 20 pages; v2: typos corrected; v3: final version with minor
corrections. To appear in IMR
A recursion and a combinatorial formula for Jack polynomials
Heckman and Opdam introduced a non-symmetric analogue of Jack polynomials
using Cherednik operators. In this paper, we derive a simple recursion formula
for these polynomials and formulas relating the symmetric Jack polynomials with
the non-symmetric ones. These formulas are then implemented by a closed
expression of symmetric and non-symmetric Jack polynomials in terms of certain
tableaux. The main application is a proof of a conjecture of Macdonald stating
certain integrality and positivity properties of Jack polynomials.Comment: Preprint March 1996, to appear in Invent. Math., 15 pages, Plain Te
- β¦