Results 21 to 30 of about 77,378 (232)

Nonsymmetric Macdonald polynomials and Demazure characters

Duke Mathematical Journal, 2003
We establish a connection between a specialization of the nonsymmetric Macdonald polynomials and the Demazure characters of the corresponding affine Kac-Moody algebra. This allows us to obtain a representation-theoretical interpretation of the coefficients of the expansion of the specialized symmetric Macdonald polynomials in the basis formed by the ...
Bogdan Ion
openalex   +5 more sources

A raising operator formula for Macdonald polynomials

Forum of Mathematics, Sigma
We give an explicit raising operator formula for the modified Macdonald polynomials $\tilde {H}_{\mu }(X;q,t)$ , which follows from our recent formula for $\nabla $ on an LLT polynomial and the Haglund-Haiman-Loehr formula expressing ...
J. Blasiak, M. Haiman, J. Morse, A. Pun, G. H. Seelinger   +4 more
doaj   +2 more sources

Higher Rank Macdonald Polynomials [PDF]

arXiv
In this paper, we introduce higher rank generalizations of Macdonald polynomials. The higher rank non-symmetric Macdonald polynomials are Laurent polynomials in several sets of variables which form weight bases for higher rank polynomial representations of double affine Hecke algebras with respect to higher rank Cherednik operators. We prove that these
Milo Bechtloff Weising
arxiv   +3 more sources

c-functions and Macdonald polynomials [PDF]

Journal of Algebra
This is a paper about $c$-functions and Macdonald polynomials. There are $c$-function formulas for $E$-expansions of $P_λ$ and $A_{λ+ρ}$, principal specializations of $P_λ$ and $E_μ$, for Macdonald's constant term formulas, and for the norms of Macdonald polynomials.
Laura Colmenarejo, Arun Ram
openalex   +3 more sources

Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials [PDF]

Selecta Mathematica, 2022
We present several new and compact formulas for the modified and integral form of the Macdonald polynomials, building on the compact "multiline queue" formula for Macdonald polynomials due to Corteel, Mandelshtam and Williams. We also introduce a new quasisymmetric analogue of Macdonald polynomials. These quasisymmetric Macdonald polynomials refine the
Corteel, Sylvie, Haglund, Jim, Mandelshtam, Olya, Mason, Sarah, Williams, Lauren   +4 more
openaire   +3 more sources

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
openaire   +3 more sources

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
doaj   +1 more source

Combinatorial Formulas for Macdonald and Hall-Littlewood Polynomials [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
A breakthrough in the theory of (type $A$) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of fillings of Young diagrams.
Cristian Lenart
doaj   +1 more source

E-Polynomials of Generic $\mathbf {\operatorname {\mathrm {GL}}_n\rtimes \!<\!\sigma \!>\!}~$ -Character Varieties: Branched Case

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
doaj   +1 more source

Motor‐induced oscillations in choice response performance

Psychophysiology, Volume 60, Issue 2, February 2023., 2023
Abstract Recently, numerous studies have revealed 4–12 Hz fluctuations of behavioral performance in a multitude of tasks. The majority has utilized stimuli near detection threshold and observed related fluctuations in hit‐rates, attributing these to perceptual or attentional processes.
Ulrich Pomper, Ulrich Ansorge
wiley   +1 more source