Results 21 to 30 of about 18,306 (234)
Type A partially-symmetric Macdonald polynomials [PDF]
Algebraic CombinatoricsWe construct type A partially-symmetric Macdonald polynomials P (λ∣γ) , where λ∈ℤ ≥0 n-k is a partition and γ∈ℤ ≥0 k is a composition. These are polynomials which are symmetric in the first n-k variables, but not necessarily in the final k variables. We establish their stability and an integral form defined using Young diagram statistics. Finally, we
Ben Goodberry
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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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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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Modified Macdonald Polynomials and Integrability [PDF]
Communications in Mathematical Physics, 2020 References corrected, explanations and examples ...
Alexandr Garbali, Michael Wheeler
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On factorization of generalized Macdonald polynomials
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, А. Морозов
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The norm and the Evaluation of the Macdonald polynomials in superspace [PDF]
European Journal of Combinatorics, 2019 We demonstrate the validity of previously conjectured explicit expressions for the norm and the evaluation of the Macdonald polynomials in superspace. These expressions, which involve the arm-lengths and leg-lengths of the cells in certain Young diagrams, specialize to the well known formulas for the norm and the evaluation of the usual Macdonald ...
Camilo González, Luc Lapointe
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Macdonald polynomials at $t=q^k$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We investigate the homogeneous symmetric Macdonald polynomials $P_{\lambda} (\mathbb{X} ;q,t)$ for the specialization $t=q^k$. We show an identity relying the polynomials $P_{\lambda} (\mathbb{X} ;q,q^k)$ and $P_{\lambda} (\frac{1-q}{1-q^k}\mathbb{X} ;q ...
Jean-Gabriel Luque
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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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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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Multi-Macdonald polynomials [PDF]
Discrete Mathematics, 2020 We introduce Macdonald polynomials indexed by $n$-tuples of partitions and characterized by certain orthogonality and triangularity relations. We prove that they can be explicitly given as products of ordinary Macdonald polynomials depending on special alphabets.
Camilo González, Luc Lapointe
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