A new tableau model for irreducible polynomial representations of the orthogonal group

2021/07/01 by Watanabe, Hideya · 1 citation
#05E10 #17B10 #17B37 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2107.00170

Abstract

We provide a new tableau model from which one can easily deduce the characters of finite-dimensional irreducible polynomial representations of the special orthogonal group SO_n(ℂ). This model originates from the representation theory of the \imathquantum group (also known as the quantum symmetric pair coideal subalgebra) of type A I, and is equipped with a combinatorial structure, which we call A I-crystal structure. This structure enables us to describe combinatorially the tensor product of an SO_n(ℂ)-module and a GL_n(ℂ)-module, and the branching from GL_n(ℂ) to SO_n(ℂ).

Cited by

• q-deformed Howe duality for orthosymplectic Lie superalgebras

Related

• Crystal bases and combinatorics of infinite rank quantum groups
• Representation theory of very non-standard quantum so(2N-1)
• Orthogonal polynomial duality and unitary symmetries of multi--species ASEP(q,\boldsymbolθ) and higher--spin vertex models via ^*--bialgebra structure of higher rank quantum groups
• Matrix factorizations and intertwiners of the fundamental representations of quantum group U_q (sl_n)
• Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux