Results 31 to 40 of about 77,378 (232)
A representation-theoretic proof of the branching rule for Macdonald polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of $U_q(gl_n)$. In the Gelfand-Tsetlin basis, we show that diagonal
Yi Sun
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Matrix product and sum rule for Macdonald polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov– Faddeev (ZF) algebra.
Luigi Cantini +2 more
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On factorization of generalized Macdonald polynomials [PDF]
The European Physical Journal C, 2016 A remarkable feature of Schur functions -- the common eigenfunctions of cut-and-join operators from $W_\infty$ -- is that they factorize at the peculiar two-parametric topological locus in the space of time-variables, what is known as the hook formula for quantum dimensions of representations of $U_q(SL_N)$ and plays a big role in various applications.
Ya. Kononov, An. Morozov, An. Morozov
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Modified Macdonald Polynomials and Integrability [PDF]
Communications in Mathematical Physics, 2020 References corrected, explanations and examples ...
Alexandr Garbali, Michael Wheeler
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A combinatorial formula for Macdonald polynomials [PDF]
Journal of the American Mathematical Society, 2005 We prove a combinatorial formula for the Macdonald polynomialH~μ(x;q,t)\tilde {H}_{\mu }(x;q,t)which had been conjectured by Haglund. Corollaries to our main theorem include the expansion ofH~μ(x;q,t)\tilde {H}_{\mu }(x;q,t)in terms of LLT polynomials, a new proof of the charge formula of Lascoux and Schützenberger for Hall-Littlewood polynomials, a ...
Mark Haiman +3 more
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A Summation Formula for Macdonald Polynomials [PDF]
Letters in Mathematical Physics, 2016 We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases $t=1$ and $q=0$, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively.
de Gier, J, Wheeler, M
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Gauge Theories and Macdonald Polynomials [PDF]
Communications in Mathematical Physics, 2012 We study the N=2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian description, we conjecture explicit formulae for all A-type quivers of class S, which in general do not have one.
Shlomo S. Razamat +4 more
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Macdonald–Koornwinder Polynomials [PDF]
, 2020 An overview of the basic results on Macdonald(-Koornwinder) polynomials and double affine Hecke algebras is given. We develop the theory in such a way that it naturally encompasses all known cases. Among the basic properties of the Macdonald polynomials we treat are the quadratic norm formulas, duality and the evaluation formulas.
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Combinatorial Formula for the Hilbert Series of bigraded $S_n$-modules [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We introduce a combinatorial way of calculating the Hilbert series of bigraded $S_n$-modules as a weighted sum over standard Young tableaux in the hook shape case.
Meesue Yoo
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A New Generalisation of Macdonald Polynomials [PDF]
Communications in Mathematical Physics, 2017 We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters $(q,t)$ and polynomial in a further two parameters $(u,v)$. We evaluate these polynomials explicitly as a matrix product.
Alexandr Garbali +2 more
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