Results 51 to 60 of about 77,378 (232)
Set-valued tableaux for Macdonald polynomials [PDF]
arXiv, 2022 Set-valued tableaux formulas play an important role in Schubert calculus. Using the box greedy reduced word for the construction of the Macdonald polynomials, we convert the alcove walk formula for Macdonald polynomials to a set-valued tableaux formula for Macdonald polynomials.
arxiv
Discrete Mathematics & Theoretical Computer Science, 2020 We conjecture two combinatorial interpretations for the symmetric function ∆eken, where ∆f is an eigenoperator for the modified Macdonald polynomials defined by Bergeron, Garsia, Haiman, and Tesler.
James Haglund +2 more
doaj +1 more source
Symmetry and Pieri rules for the bisymmetric Macdonald polynomials [PDF]
arXiv, 2023 Bisymmetric Macdonald polynomials can be obtained through a process of antisymmetrization and $t$-symmetrization of non-symmetric Macdonald polynomials. Using the double affine Hecke algebra, we show that the evaluation of the bisymmetric Macdonald polynomials satisfies a symmetry property generalizing that satisfied by the usual Macdonald polynomials.
arxiv
Hypergeometric theta functions and elliptic Macdonald polynomials [PDF]
International Mathematics Research Notices (2004) 2004:1037-1055, 2003 Elliptic Macdonald polynomials of sl(2)-type and level 2 are introduced. Suitable limits of elliptic Macdonald polynomials are the standard Macdonald polynomials and conformal blocks. Identities for elliptic Macdonald polynomials, in particular their modular properties, are studied.
arxiv +1 more source
Recursions and divisibility properties for combinatorial Macdonald polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Combinatorics
Nicholas A. Loehr, Elizabeth Niese
doaj +1 more source
Canonical Basis and Macdonald Polynomials
Advances in Mathematics, 1998 In the basic representation of $U_q(\hat{sl}(2))$ realized via the algebra of symmetric functions we compare the canonical basis with the basis of Macdonald polynomials with $q=t^2$. We show that the Macdonald polynomials are invariant with respect to the bar involution defined abstractly on the representations of quantum groups. We also prove that the
Jonathan Beck +2 more
openaire +3 more sources
c-functions and Macdonald polynomials [PDF]
arXiv, 2022 This is a paper about $c$-functions and Macdonald polynomials. There are $c$-function formulas for $E$-expansions of $P_\lambda$ and $A_{\lambda+\rho}$, principal specializations of $P_\lambda$ and $E_\mu$, for Macdonald's constant term formulas, and for the norms of Macdonald polynomials.
arxiv
An extension of MacMahon's Equidistribution Theorem to ordered multiset partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A classical result of MacMahon states that inversion number and major index have the same distribution over permutations of a given multiset. In this work we prove a strengthening of this theorem originally conjectured by Haglund.
Andrew Timothy Wilson
doaj +1 more source
Shiraishi functor and non-Kerov deformation of Macdonald polynomials
European Physical Journal C: Particles and Fields, 2020 We suggest a further generalization of the hypergeometric-like series due to M. Noumi and J. Shiraishi by substituting the Pochhammer symbol with a nearly arbitrary function.
Hidetoshi Awata +3 more
doaj +1 more source
On pentagon identity in Ding-Iohara-Miki algebra
Journal of High Energy Physics, 2023 We notice that the famous pentagon identity for quantum dilogarithm functions and the five-term relation for certain operators related to Macdonald polynomials discovered by Garsia and Mellit can both be understood as specific cases of a general “master ...
Yegor Zenkevich
doaj +1 more source