Bounded Littlewood Identities
Title | Bounded Littlewood Identities PDF eBook |
Author | Eric M. Rains |
Publisher | American Mathematical Soc. |
Pages | 115 |
Release | 2021-07-21 |
Genre | Education |
ISBN | 1470446901 |
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.
BOUNDED LITTLEWOOD IDENTITIES.
Title | BOUNDED LITTLEWOOD IDENTITIES. PDF eBook |
Author | ERIC M. RAINS |
Publisher | |
Pages | |
Release | 2021 |
Genre | |
ISBN | 9781470465223 |
Non-Kissing Complexes and Tau-Tilting for Gentle Algebras
Title | Non-Kissing Complexes and Tau-Tilting for Gentle Algebras PDF eBook |
Author | Yann Palu |
Publisher | American Mathematical Society |
Pages | 95 |
Release | 2021-12-30 |
Genre | Mathematics |
ISBN | 1470450046 |
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Cubic Action of a Rank One Group
Title | Cubic Action of a Rank One Group PDF eBook |
Author | Matthias Grüninger |
Publisher | American Mathematical Society |
Pages | 154 |
Release | 2022-04-08 |
Genre | Mathematics |
ISBN | 1470451344 |
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Local $L^p$-Brunn-Minkowski Inequalities for $p
Title | Local $L^p$-Brunn-Minkowski Inequalities for $p PDF eBook |
Author | Alexander V. Kolesnikov |
Publisher | American Mathematical Society |
Pages | 78 |
Release | 2022-05-24 |
Genre | Mathematics |
ISBN | 1470451603 |
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On the Symplectic Type of Isomorphisms of the $p$-Torsion of Elliptic Curves
Title | On the Symplectic Type of Isomorphisms of the $p$-Torsion of Elliptic Curves PDF eBook |
Author | Nuno Freitas |
Publisher | American Mathematical Society |
Pages | 105 |
Release | 2022-05-24 |
Genre | Mathematics |
ISBN | 1470452103 |
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Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups
Title | Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups PDF eBook |
Author | Pierre Patie |
Publisher | American Mathematical Society |
Pages | 182 |
Release | 2021-11-16 |
Genre | Mathematics |
ISBN | 1470449366 |
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