2005
DOI: 10.1007/s00031-005-1003-y
|View full text |Cite
|
Sign up to set email alerts
|

BCn-symmetric polynomials

Abstract: We consider two important families of BCn-symmetric polynomials, namely Okounkov's interpolation polynomials and Koornwinder's orthogonal polynomials. We give a family of difference equations satisfied by the former as well as generalizations of the branching rule and Pieri identity, leading to a number of multivariate q-analogues of classical hypergeometric transformations. For the latter, we give new proofs of Macdonald's conjectures, as well as new identities, including an inverse binomial formula and sever… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

2
192
0
1

Year Published

2007
2007
2024
2024

Publication Types

Select...
8

Relationship

3
5

Authors

Journals

citations
Cited by 82 publications
(198 citation statements)
references
References 20 publications
(8 reference statements)
2
192
0
1
Order By: Relevance
“…The motivation for the machinery developed in this paper arose when the first author was investigating certain conjectures involving Macdonald polynomials generalizing classical identities of Schur functions related to the representation theory of symmetric spaces [9]. These Schur function identities are closely related to Littlewood identities and thus via invariant theory [1, §8] to the action of S 2n by conjugation on fixed-point-free involutions.…”
Section: Introductionmentioning
confidence: 99%
“…The motivation for the machinery developed in this paper arose when the first author was investigating certain conjectures involving Macdonald polynomials generalizing classical identities of Schur functions related to the representation theory of symmetric spaces [9]. These Schur function identities are closely related to Littlewood identities and thus via invariant theory [1, §8] to the action of S 2n by conjugation on fixed-point-free involutions.…”
Section: Introductionmentioning
confidence: 99%
“…In this section, we prove four other vanishing identities from [20] and [18]. In all four cases, the structure of the partition that produces a nonvanishing integral is the same: opposite parts must add to zero (λ i + λ l+1−i = 0 for all 1 ≤ i ≤ l, where l is the total number of parts).…”
Section: Other Vanishing Resultsmentioning
confidence: 89%
“…We find a two-parameter integral identity and, using a method of Rains [18], we show that in the limit n → ∞ it becomes Warnaar's identity. Thus, the following identity may be viewed as a finite-dimensional analog of Warnaar's summation result: Theorem 1.9.…”
Section: Another Nice Consequence Of Our Technique Involves a Recent mentioning
confidence: 82%
See 1 more Smart Citation
“…The latter are specific 2 φ 1 series, see (7.1), which when principally specialized simplify to ratios of q-shifted factorials by virtue of the Chu-Vandermonde summation theorem, the terminating special case of the q-Gauß summation in (3.2). We mention that for the nonreduced irreducible root system BC n very-well-poised basic hypergeometric series identities involving Okounkov's [44] Macdonald interpolation polynomials or the more general Koornwinder-Macdonald polynomials (both which are of BC n type) have been established by Rains, see [45,Sec. 4] and [46,Sec.…”
Section: More Basic Hypergeometric Identities Involving Macdonald Polmentioning
confidence: 99%