BCn-symmetric polynomials
By Eric M. Rains. 2001
84 citations recorded by the source corpus.
AbstractWe 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 several branching rule and connection coefficient identities. We also derive families of ordinary symmetric functions that reduce to the interpolation and Koornwinder polynomials upon appropriate specialization. As an application, we consider a number of new integral conjectures associated to classical symmetric spaces.
Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/8d6fe0763aa88ee741fd818823abc72122c074a8
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In Algebra and Number Theory
- Eric M. Rains
- A. Litvinov
- V. Fateev
- G. Tarnopolskiy
- Vasyl Alba
- V. Spiridonov
- Alexei Borodin
- Gérard Ben Arous
In Applied Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- On Combinatorial Expansion of the Conformal Blocks Arising from AGT Conjecture (2010, background): “14) (8)The notation f [sk] (square brackets instead of parentheses) is known in symmetric functions theory as plethystic substitution [39].”
- $BC_n$-symmetric abelian functions (2004, background): “ument and index are interchanged via this symmetry. The special form of the bigrid in our case gives rise to another symmetry as well, which follows from a computation along the lines of Lemma 2.1 of [16]: P∗(m,n) µ (λ;a,pq/qmtna;q,t;p) = C0 mn (t n;q,t;p) C 0 mn(q−m;q,t;p) C0 λ (q mt2n−1a2,(pq/t)tn”