Weyl algebras for quantum homogeneous spaces

Abstract

We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given size. The construction uses twisted tensor products and their deformations combined with invariance properties derived from quantum symmetric pairs. These quantum Weyl algebras admit $U_q({\mathfrak{gl}}_N)$-module algebra structures compatible with standard ones on the polynomial part, have relations that are expressed nicely via matrices, and are closely related to an algebra arising in the theory of quantum bounded symmetric domains.

References in corpus (6)

• Quantum symmetric Kac-Moody pairs
• Difference equations and symmetric polynomials defined by their zeros
• Symmetric and non-symmetric quantum Capelli polynomials
• Poincare-Birkhoff-Witt deformations of smash product algebras from Hopf actions on Koszul algebras
• Quantum Weyl algebras and reflection equation algebras at a root of unity
• On a q-analog of a Sahi result

Cited by in corpus (1)

• Quantized Weyl algebras, the double centralizer property, and a new First Fundamental Theorem for $U_q({\mathfrak{gl}}_n)$