Author: Eric M. Rains
Publisher: American Mathematical Soc.
ISBN: 1470446901
Category : Education
Languages : en
Pages : 115
Book Description
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
Author: Eric M. Rains
Publisher: American Mathematical Soc.
ISBN: 1470446901
Category : Education
Languages : en
Pages : 115
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 1470446901
Category : Education
Languages : en
Pages : 115
Book Description
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.
Author: ERIC M. RAINS
Publisher:
ISBN: 9781470465223
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN: 9781470465223
Category :
Languages : en
Pages :
Book Description
Local $L^p$-Brunn-Minkowski Inequalities for $p
Author: Alexander V. Kolesnikov
Publisher: American Mathematical Society
ISBN: 1470451603
Category : Mathematics
Languages : en
Pages : 78
Book Description
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Publisher: American Mathematical Society
ISBN: 1470451603
Category : Mathematics
Languages : en
Pages : 78
Book Description
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On the Symplectic Type of Isomorphisms of the $p$-Torsion of Elliptic Curves
Author: Nuno Freitas
Publisher: American Mathematical Society
ISBN: 1470452103
Category : Mathematics
Languages : en
Pages : 105
Book Description
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Publisher: American Mathematical Society
ISBN: 1470452103
Category : Mathematics
Languages : en
Pages : 105
Book Description
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Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups
Author: Pierre Patie
Publisher: American Mathematical Society
ISBN: 1470449366
Category : Mathematics
Languages : en
Pages : 182
Book Description
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Publisher: American Mathematical Society
ISBN: 1470449366
Category : Mathematics
Languages : en
Pages : 182
Book Description
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On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function
Author: Athanassios S. Fokas
Publisher: American Mathematical Society
ISBN: 1470450984
Category : Mathematics
Languages : en
Pages : 114
Book Description
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Publisher: American Mathematical Society
ISBN: 1470450984
Category : Mathematics
Languages : en
Pages : 114
Book Description
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Intense Automorphisms of Finite Groups
Author: Mima Stanojkovski
Publisher: American Mathematical Society
ISBN: 1470450038
Category : Mathematics
Languages : en
Pages : 117
Book Description
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Publisher: American Mathematical Society
ISBN: 1470450038
Category : Mathematics
Languages : en
Pages : 117
Book Description
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The Canonical Ring of a Stacky Curve
Author: John Voight
Publisher: American Mathematical Society
ISBN: 1470452286
Category : Mathematics
Languages : en
Pages : 142
Book Description
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Publisher: American Mathematical Society
ISBN: 1470452286
Category : Mathematics
Languages : en
Pages : 142
Book Description
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Souslin Quasi-Orders and Bi-Embeddability of Uncountable Structures
Author: Alessandro Andretta
Publisher: American Mathematical Society
ISBN: 1470452731
Category : Mathematics
Languages : en
Pages : 189
Book Description
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Publisher: American Mathematical Society
ISBN: 1470452731
Category : Mathematics
Languages : en
Pages : 189
Book Description
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Brownian Regularity for the Airy Line Ensemble, and Multi-Polymer Watermelons in Brownian Last Passage Percolation
Author: Alan Hammond
Publisher: American Mathematical Society
ISBN: 1470452294
Category : Mathematics
Languages : en
Pages : 131
Book Description
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Publisher: American Mathematical Society
ISBN: 1470452294
Category : Mathematics
Languages : en
Pages : 131
Book Description
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