Multiplication formula for Hernandez and Leclerc's quivers with potentials

Yingjin Bi

Multiplication formula for Hernandez and Leclerc's quivers with potentials

Representation Theory 2024-07-12 v2 Quantum Algebra Rings and Algebras

Authors: Yingjin Bi

Abstract

In this paper, we study multiplication formula of $F$ -polynomial of representations of Hernandez and Leclerc's quivers with potentials. Since the truncated $q$ -characters of some real simple modules over a quantum affine group $U_q(\widehat{\mathfrak{g}})$ can be expressed in terms of such $F$ -polynomials, one can describe the product of two simple modules over $U_q(\widehat{\mathfrak{g}})$ using this multiplication formula.

Keywords

q-series and q-analogues kazhdan-lusztig polynomials

Cite

@article{arxiv.2405.11232,
  title  = {Multiplication formula for Hernandez and Leclerc's quivers with potentials},
  author = {Yingjin Bi},
  journal= {arXiv preprint arXiv:2405.11232},
  year   = {2024}
}

Comments

There is an error: In section 2. Jacobian algebras do in general NOT enjoy the Ext-symmetry which was crucial for the GLS multiplication formula. Morevor, the generalized preprojective are in general NOT Jacobian algebras because the nilpotency relations of the loops don't come from the potential

Multiplication formula for Hernandez and Leclerc's quivers with potentials

Abstract

Keywords

Cite

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