On irreducibility of tensor products of evaluation modules for the quantum affine algebra

Abstract

Every irreducible finite-dimensional representation of the quantized enveloping algebra U_q(gl_n) can be extended to the corresponding quantum affine algebra via the evaluation homomorphism. We give in explicit form the necessary and sufficient conditions for irreducibility of tensor products of such evaluation modules.

22 pages. Some references are added

References in corpus (7)

• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• On the quantum inverse scattering problem
• Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras
• Finite-dimensional irreducible representations of twisted Yangians
• Braid Group Actions and Tensor Products
• Quiver Varieties and Yangians
• Spinor Representations of $U_q(\widehat{\mathfrak{g}l}(n))$ and Quantum Boson-Fermion Correspondence

Cited by in corpus (7)

• Quantum affine Gelfand-Tsetlin bases and quantum toroidal algebra via K-theory of affine Laumon spaces
• Irreducible representations of Yangians
• Braid group actions and tensor products for Yangians
• Gelfand-Tsetlin algebras and cohomology rings of Laumon spaces
• Dual canonical bases for the quantum special linear group and invariant subalgebras
• Representations of quantum affine algebras of type $B_N$
• Finite dimensional simple modules of $(q,\mathbf{Q})$-current algebras