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In this paper we construct Young wall models for the level $1$ highest weight and Fock space crystals of quantum affine algebras in types $E_6^{(2)}$ and $F_4^{(1)}$. Our starting point in each case is a combinatorial realization for a certain level
Externí odkaz:
http://arxiv.org/abs/2402.15829
Autor:
Laurie, Duncan
We construct Young wall models for the crystal bases of level $1$ irreducible highest weight representations and Fock space representations of quantum affine algebras in types $E_{6}^{(1)}$, $E_{7}^{(1)}$ and $E_{8}^{(1)}$. In each case, Young walls
Externí odkaz:
http://arxiv.org/abs/2311.03905
Autor:
Laurie, Duncan
We first construct an action of the extended double affine braid group $\mathcal{\ddot{B}}$ on the quantum toroidal algebra $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in untwisted and twisted types. As a crucial step in the proof, we obtain a finite Drinfe
Externí odkaz:
http://arxiv.org/abs/2304.06773
Autor:
Laurie, Duncan
Publikováno v:
In Journal of Algebra 1 January 2025 661:430-478