Strong Duality Data of Type A and Extended T-Systems

2024/05/15 by Katsuyuki Naoi · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Algebra and Geometry

paper · pdf · doi:10.1007/s00031-024-09860-5

Abstract

Abstract The extended T -systems are a number of relations in the Grothendieck ring of the category of finite-dimensional modules over the quantum affine algebras of types A_n⁽¹⁾ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>n</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> and B_n⁽¹⁾ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>n</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> , introduced by Mukhin and Young as a generalization of the T -systems. In this paper we establish the extended T -systems for more general modules, which are constructed from an arbitrary strong duality datum of type A . Our approach does not use the theory of q -characters, and so also provides a new proof to the original Mukhin–Young’s extended T -systems.

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