Bounded Littlewood identities

Bounded Littlewood identities

"We describe a method, based on the theory of Macdonald-Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald's partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polyno...

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Détails bibliographiques
Auteurs principaux : Rains Eric M. (Auteur), Warnaar S. Ole (Auteur)
Format : Livre
Langue : anglais
Titre complet : Bounded Littlewood identities / Eric M. Rains, S. Ole Warnaar
Publié : Providence, RI : American Mathematical Society , 2021
Description matérielle : 1 vol. (vii-115 pages)
Collection : Memoirs of the American Mathematical Society
Contenu : Introduction: Littlewood identities ; Outline. Macdonald-Koornwinder theory. Virtual Koornwinder integrals. Bounded Littlewood identities. Applications. Open problems. Appendix A. The Weyl-Kac formula. Appendix B. Limits of elliptic hypergeometric integrals
Sujets :
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225 2 |a Memoirs of the American Mathematical Society  |x 0065-9266  |v number 1317 
303 |a "March 2021, volume 270, number 1317 (first of 7 numbers)." 
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327 1 |a Introduction: Littlewood identities ; Outline  |a Macdonald-Koornwinder theory  |a Virtual Koornwinder integrals  |a Bounded Littlewood identities  |a Applications  |a Open problems  |a Appendix A. The Weyl-Kac formula  |a Appendix B. Limits of elliptic hypergeometric integrals 
330 |a "We describe a method, based on the theory of Macdonald-Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald's partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R, S) in terms of ordinary Macdonald polynomials, are q, t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups. In the classical limit, our method implies that MacMahon's famous ex-conjecture for the generating function of symmetric plane partitions in a box follows from the identification of GL(n, R), O(n) as a Gelfand pair. As further applications, we obtain combinatorial formulas for characters of affine Lie algebras; Rogers-Ramanujan identities for affine Lie algebras, complementing recent results of Griffin et al.; and quadratic transformation formulas for Kaneko-Macdonald-type basic hypergeometric series." -- page 5 
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