AbstractA unified theory of quantum symmetric pairs is applied to q-special functions. Previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal spherical functions. Here a distinguished family of such functions, invariant under the Weyl group associated to the restricted roots, is shown to be a family of Macdonald polynomials, as conjectured by Koornwinder and Macdonald. Our results place earlier work for Lie algebras of classical type in a general context and extend to the exceptional cases
The $SL(2,\mathbb Z)$-symmetry of Cherednik's spherical double affine Hecke algebras in Macdonald th...
AbstractIn the basic representation of[formula]realized via the algebra of symmetric functions, we c...
We construct a novel family of difference-permutation operators and prove that they are diagonalized...
AbstractThe spaces of invariants and the zonal spherical functions associated with quantum super 2-s...
The presented thesis describes a new family of spherical right coideal subalgebras of quantum univer...
Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of ...
We introduce and study quantum Capelli operators inside newly constructed quantum Weyl algebras asso...
We give an explicit description of the zonal spherical functions on quantum Grassmann manifolds of o...
We give an explicit description of the zonal spherical functions on quantum Grassmann manifolds of o...
AbstractThe representation theory of symmetric Lie superalgebras and corresponding spherical functio...
We introduce new families of cylindric symmetric functions as subcoalgebras in the ring of symmetric...
The presented thesis describes a new family of spherical right coideal subalgebras of quantum univer...
We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of ...
The SL(2, Z)-symmetry of Cherednik's spherical double affine Hecke algebras in Macdonald theory incl...
AbstractLet θ be an involution of a semisimple Lie algebra g, let gθ denote the fixed Lie subalgebra...
The $SL(2,\mathbb Z)$-symmetry of Cherednik's spherical double affine Hecke algebras in Macdonald th...
AbstractIn the basic representation of[formula]realized via the algebra of symmetric functions, we c...
We construct a novel family of difference-permutation operators and prove that they are diagonalized...
AbstractThe spaces of invariants and the zonal spherical functions associated with quantum super 2-s...
The presented thesis describes a new family of spherical right coideal subalgebras of quantum univer...
Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of ...
We introduce and study quantum Capelli operators inside newly constructed quantum Weyl algebras asso...
We give an explicit description of the zonal spherical functions on quantum Grassmann manifolds of o...
We give an explicit description of the zonal spherical functions on quantum Grassmann manifolds of o...
AbstractThe representation theory of symmetric Lie superalgebras and corresponding spherical functio...
We introduce new families of cylindric symmetric functions as subcoalgebras in the ring of symmetric...
The presented thesis describes a new family of spherical right coideal subalgebras of quantum univer...
We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of ...
The SL(2, Z)-symmetry of Cherednik's spherical double affine Hecke algebras in Macdonald theory incl...
AbstractLet θ be an involution of a semisimple Lie algebra g, let gθ denote the fixed Lie subalgebra...
The $SL(2,\mathbb Z)$-symmetry of Cherednik's spherical double affine Hecke algebras in Macdonald th...
AbstractIn the basic representation of[formula]realized via the algebra of symmetric functions, we c...
We construct a novel family of difference-permutation operators and prove that they are diagonalized...