Results 11 to 20 of about 427 (182)
Vector-Valued Jack Polynomials from Scratch [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 Vector-valued Jack polynomials associated to the symmetric group S_N are polynomials with multiplicities in an irreducible module of S_N and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators with some additional properties concerning
Jean-Gabriel Luque, Charles F. Dunkl
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Jack Polynomials in Superspace [PDF]
Communications in Mathematical Physics, 2003 This work initiates the study of {\it orthogonal} symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric ...
Desrosiers, P. +2 more
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A superpolynomial version of nonsymmetric Jack polynomials [PDF]
The Ramanujan Journal, 2021 Superpolynomials consist of commuting and anti-commuting variables. By considering the anti-commuting variables as a module of the symmetric group the theory of vector-valued nonsymmetric Jack polynomials can be specialized to superpolynomials. The theory significantly differs from the supersymmetric Jack polynomials introduced and studied in several ...
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Determinantal Expression and Recursion for Jack Polynomials [PDF]
The Electronic Journal of Combinatorics, 1999 We describe matrices whose determinants are the Jack polynomials expanded in terms of the monomial basis. The top row of such a matrix is a list of monomial functions, the entries of the sub-diagonal are of the form $-(r\alpha+s)$, with $r$ and $s \in {\bf N^+}$, the entries above the sub-diagonal are non-negative integers, and below all entries are ...
Lapointe, L., Lascoux, Alain, Morse, J.
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Highest weight Macdonald and Jack polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2011 17 pages, published ...
Jolicoeur, Th., Luque, Jean-Gabriel
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New Pieri Type Formulas for Jack Polynomials and their Applications to Interpolation Jack Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2020 We present new Pieri type formulas for Jack polynomials. As an application, we give a new derivation of higher order difference equations for interpolation Jack polynomials originally found by Knop and Sahi. We also propose Pieri formulas for interpolation Jack polynomials and intertwining relations for a kernel function for Jack polynomials.
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From Jack to Double Jack Polynomials via the Supersymmetric Bridge [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2015 The Calogero-Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. The supersymmetric counterpart of this model, although much less ubiquitous, has an equally rich structure. In particular, its eigenfunctions, the Jack superpolynomials, appear to share the very same remarkable ...
Lapointe, L., Mathieu, P.
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Super Jack-Laurent Polynomials [PDF]
Algebras and Representation Theory, 2018 29 pages, Corrected typos, Added ...
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AGT basis in SCFT for c = 3/2 and Uglov polynomials
Nuclear Physics B, 2020 AGT allows one to compute conformal blocks of d = 2 CFT for a large class of chiral CFT algebras. This is related to the existence of a certain orthogonal basis in the module of the (extended) chiral algebra. The elements of the basis are eigenvectors of
Vladimir Belavin, Abay Zhakenov
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European Physical Journal C: Particles and Fields, 2023 Since the ( $$\beta $$ β -deformed) Hurwitz Kontsevich model corresponds to the special case of affine Yangian of $${\mathfrak {gl}}(1)$$ gl ( 1 ) . In this paper, we construct two general cases of the $$\beta $$ β -deformed Hurwitz Kontsevich model.
Wang Na, Wu Ke
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