Branching rules for quantum toroidal gl(n)

Abstract

We construct an analog of the subalgebra $Ugl(n)\otimes Ugl(m)$ of $Ugl(m+n)$ in the setting of quantum toroidal algebras and study the restrictions of various representations to this subalgebra.

Latex, 38 pages, misprints corrected

References in corpus (1)

• Quantum toroidal ${\mathfrak{gl}}_1$ algebra : plane partitions

Cited by in corpus (14)

• Ding-Iohara-Miki symmetry of network matrix models
• Explicit examples of DIM constraints for network matrix models
• W-algebras as coset vertex algebras
• Cohomological Hall algebras, vertex algebras and instantons
• Quiver Yangian from Crystal Melting
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Integrals of motion from quantum toroidal algebras
• Instanton R-matrix and W-symmetry
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• Homomorphisms between different quantum toroidal and affine Yangian algebras
• The $({\mathfrak{gl}}_m,{\mathfrak{gl}}_n$) duality in the quantum toroidal setting
• Twisted Representations of Algebra of $q$-Difference Operators, Twisted $q$-$W$ Algebras and Conformal Blocks
• Quantum toroidal algebras and motivic Hall algebras I. Hall algebras for singular elliptic curves
• Level $-1/2$ realization of quantum N-toroidal algebras in type $C_n$