Results 21 to 30 of about 427 (182)
Towards the Calculation of Jack Polynomials [PDF]
, 2021 <p>Jack polynomials are useful in mathematical statistics, but they are awkward to calculate, and their uses have chiefly been theoretical. In this thesis a determinantal expansion of Jack polynomials in elementary symmetric polynomials is found, complementing a recent result in the literature on expansions as determinants in monomial symmetric ...
openaire +1 more source
Superanalogs of the Calogero Operators and Jack Polynomials [PDF]
Journal of Nonlinear Mathematical Physics, 2001 A depending on a complex parameter $k$ superanalog ${\mathcal S}{\mathcal L}$ of Calogero operator is constructed; it is related with the root system of the Lie superalgebra ${\mathfrak{gl}}(n|m)$. For $m=0$ we obtain the usual Calogero operator; for $m=1$ we obtain, up to a change of indeterminates and parameter $k$ the operator constructed by Veselov,
openaire +2 more sources
Creation Operators for the Macdonald and Jack Polynomials
Letters in Mathematical Physics, 1997 14 pages ...
Lapointe, Luc, Vinet, Luc
openaire +3 more sources
An Analytic Formula for the A 2 Jack Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
openaire +5 more sources
Applications of a Laplace–Beltrami operator for Jack polynomials
European Journal of Combinatorics, 2012 We use a new method to study the Laplace-Beltrami type operator on the Fock space of symmetric functions, and as an example of our explicit computation we show that the Jack symmetric functions are the only family of eigenvectors of the differential operator.
Wuxing Cai, Naihuan Jing
openaire +2 more sources
Virasoro irregular conformal block and beta deformed random matrix model
Physics Letters B, 2015 Virasoro irregular conformal block is presented as the expectation value of Jack-polynomials of the beta-deformed Penner-type matrix model and is compared with the inner product of Gaiotto states with arbitrary rank.
Sang Kwan Choi, Chaiho Rim, Hong Zhang
doaj +1 more source
Affine Yangian and 3-Schur functions
Nuclear Physics B, 2020 3D (3 dimensional) Young diagram is a generalization of 2D Young diagram. In this paper, from the orthogonality of 3D Young diagrams and the properties in affine Yangian and its MacMahon representation, we obtain the Schur functions corresponding to 3D ...
Na Wang
doaj +1 more source
A Unified View of Determinantal Expansions for Jack Polynomials [PDF]
The Electronic Journal of Combinatorics, 2000 Recently Lapointe et. al. [3] have expressed Jack Polynomials as determinants in monomial symmetric functions $m_\lambda$. We express these polynomials as determinants in elementary symmetric functions $e_\lambda$, showing a fundamental symmetry between these two expansions. Moreover, both expansions are obtained indifferently by applying the Calogero-
openaire +2 more sources
Wave functions for fractional Chern insulators in disk geometry
New Journal of Physics, 2015 Recently, fractional Chern insulators (FCIs), also called fractional quantum anomalous Hall (FQAH) states, have been theoretically established in lattice systems with topological flat bands.
Ai-Lei He +3 more
doaj +1 more source