l Linear recurrence relations in Q-systems via lattice points in polyhedra
Speaker
l 이철희
Institute
l University of Queensland
Date
l 2016-02-12(Fri)
Time
l 14:00~15:00
Place
l E6-1 #1409
VodLink
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There exists an interesting family of finite-dimensional representations called the Kirillov-Reshetikhin modules over the quantum affine algebra $U_q(\widehat{\mathfrak{g}})$. The isotypic decomposition of theses modules or their tensor products as $U_q(\mathfrak{g})$-modules is given by the fermionic formula which can be regarded as a representation theoretic version of completeness of the Bethe ansatz.
In spite of its elegance, it quickly becomes impractical as the rank of $\mathfrak{g}$ increases due to its complicated combinatorial nature. Thus it is advantageous to have a more explicit description of this decomposition for practical purposes. Such a formula is well-known in classical types, but remains largely conjectural in exceptional types.
In this talk, I will talk about linear recurrence relations satisfied by the sequence $\{Q_m^{(a)}\}_{m=0}^{\infty}$ of the characters of the Kirillov-Reshetikhin modules and how they shed light on the above problem. The key idea is to regard this decomposition as a summation over the lattices points in a suitable polyhedron.
Seminar
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