Zobrazeno 1 - 10
of 245
pro vyhledávání: '"Dunkl, Charles F."'
Autor:
Dunkl, Charles F.
Publikováno v:
J Phys A. Math. Theor. 56 (2023) 375301, 23 pp
The Dunkl Laplacian is used to define the Hamiltonian of a modified quantum harmonic oscillator, associated with any finite reflection group. The potential is a sum of the inverse squares of the linear functions whose zero sets are the mirrors of the
Externí odkaz:
http://arxiv.org/abs/2302.10740
Autor:
Dunkl, Charles F.
Publikováno v:
SIGMA 19 (2023), 025, 18 pages
The two-dimensional quantum harmonic oscillator is modified with reflection terms associated with the action of the Coxeter group $B_2$, which is the symmetry group of the square. The angular momentum operator is also modified with reflections. The w
Externí odkaz:
http://arxiv.org/abs/2210.14180
Autor:
Dunkl, Charles F.
The affine Hecke algebra of type $A$ has two parameters $\left( q,t\right) $ and acts on polynomials in $N$ variables. There are two important pairwise commuting sets of elements in the algebra: the Cherednik operators and the Jucys-Murphy elements w
Externí odkaz:
http://arxiv.org/abs/2111.13618
Autor:
Dunkl, Charles F.
Publikováno v:
Symmetry 2021, 13 (5), 779
In a preceding paper the theory of nonsymmetric Macdonald polynomials taking values in modules of the Hecke algebra of type $A$ (Dunkl and Luque SLC 2012) was applied to such modules consisting of polynomials in anti-commuting variables, to define no
Externí odkaz:
http://arxiv.org/abs/2104.00710
Autor:
Dunkl, Charles F.
Publikováno v:
SIGMA 17 (2021), 054, 29 pages
There are representations of the type-A Hecke algebra on spaces of polynomials in anti-commuting variables. Luque and the author [S\'em. Lothar. Combin. 66 (2012), Art. B66b, 68 pages, arXiv:1106.0875] constructed nonsymmetric Macdonald polynomials t
Externí odkaz:
http://arxiv.org/abs/2011.05886
Autor:
Dunkl, Charles F.
Publikováno v:
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 t
Externí odkaz:
http://arxiv.org/abs/2008.13666
Autor:
Dunkl, Charles F.
Publikováno v:
Symmetry 2020 12(4), 630
In the intersection of the theories of nonsymmetric Jack polynomials in $N$ variables and representations of the symmetric groups $\mathcal{S}_{N}$ one finds the singular polynomials. For certain values of the parameter $\kappa$ there are Jack polyno
Externí odkaz:
http://arxiv.org/abs/2003.01646