Results 31 to 40 of about 561,255 (240)
A combinatorial approach to Macdonald q, t-symmetry via the Carlitz bijection [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We investigate the combinatorics of the symmetry relation H μ(x; q, t) = H μ∗ (x; t, q) on the transformed Macdonald polynomials, from the point of view of the combinatorial formula of Haglund, Haiman, and Loehr in terms of the inv and maj statistics on ...
Maria Monks Gillespie
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Forum of Mathematics, Sigma, 2023 For any branched double covering of compact Riemann surfaces, we consider the associated character varieties that are unitary in the global sense, which we call $\operatorname {\mathrm {GL}}_n\rtimes \!}$ -character varieties.
Cheng Shu
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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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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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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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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 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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Nonsymmetric Macdonald polynomials via integrable vertex models [PDF]
Transactions of the American Mathematical Society, 2019 Starting from an integrable rank-$n$ vertex model, we construct an explicit family of partition functions indexed by compositions $\mu = (\mu_1,\dots,\mu_n)$.
A. Borodin, M. Wheeler
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