A quantum cluster algebra approach to representations of simply laced quantum affine algebras
Sign Up to like & getrecommendations! Published in 2020 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-020-02664-9
Abstract: We establish a quantum cluster algebra structure on the quantum Grothendieck ring of a certain monoidal subcategory of the category of finite-dimensional representations of a simply-laced quantum affine algebra. Moreover, the (q, t)-characters of certain irreducible… read more here.
Keywords: cluster algebra; quantum; quantum cluster; quantum affine ... See more keywords
Categorical Relations Between Langlands Dual Quantum Affine Algebras: Exceptional Cases
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03287-w
Abstract: We first compute the denominator formulas for quantum affine algebras of all exceptional types. Then we prove the isomorphisms among Grothendieck rings of categories $${C_Q^{(t)} (t=1,2,3), \mathscr{C}_{\mathscr{Q}}^{(1)}}$$CQ(t)(t=1,2,3),CQ(1) and $${\mathscr{C}_{\mathfrak{Q}}^{(1)}}$$CQ(1). These results give Dorey’s rule for… read more here.
Keywords: relations langlands; algebras exceptional; quantum affine; affine algebras ... See more keywords
Quasi Modules for the Quantum Affine Vertex Algebra in Type A
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03291-0
Abstract: We consider the quantum affine vertex algebra $${\mathcal{V}_{c}(\mathfrak{gl}_N)}$$Vc(glN) associated with the rational R-matrix, as defined by Etingof and Kazhdan. We introduce certain subalgebras $${\textrm{A}_c (\mathfrak{gl}_N)}$$Ac(glN) of the completed double Yangian $${\widetilde{\textrm{DY}}_{c}(\mathfrak{gl}_N)}$$DY~c(glN) at the level $${c\in\mathbb{C}}$$c∈C,… read more here.
Keywords: affine vertex; vertex algebra; mathfrak gln; quantum affine ... See more keywords
Weight-Finite Modules Over the Quantum Affine and Double Quantum Affine Algebras of Type $\mathfrak a_{1}$
Sign Up to like & getrecommendations! Published in 2021 at "Algebras and Representation Theory"
DOI: 10.1007/s10468-021-10080-8
Abstract: We define the categories of weight-finite modules over the type $\mathfrak a_1$ quantum affine algebra $\dot{\mathrm{U}}_q(\mathfrak a_1)$ and over the type $\mathfrak a_1$ double quantum affine algebra $\ddot{\mathrm{U}}_q(\mathfrak a_1)$ that we introduced in a previous… read more here.
Keywords: mathfrak; double quantum; weight finite; quantum affine ... See more keywords
R-matrix realization of two-parameter quantum affine algebra Ur,s(glˆn)
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2017.05.028
Abstract: We introduce the two-parameter quantum affine algebra Ur,s(glˆn) via the RTT realization. The Drinfeld realization is given and the type A quantum affine algebra is proved to be a special subalgebra of our extended algebra. read more here.
Keywords: affine algebra; algebra; realization; quantum affine ... See more keywords
Principal subspaces for the quantum affine vertex algebra in type A1(1)
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Pure and Applied Algebra"
DOI: 10.1016/j.jpaa.2021.106973
Abstract: By using the ideas of Feigin and Stoyanovsky and Calinescu, Lepowsky and Milas we introduce and study the principal subspaces associated with the Etingof-Kazhdan quantum affine vertex algebra of integer level $k\geqslant 1$ and type… read more here.
Keywords: affine vertex; principal subspaces; vertex algebra; quantum affine ... See more keywords
Geometric Realization of Dynkin Quiver Type Quantum Affine Schur–Weyl Duality
Sign Up to like & getrecommendations! Published in 2018 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rny226
Abstract: For a Dynkin quiver $Q$ of type ADE and a sum $\beta$ of simple roots, we construct a bimodule over the quantum loop algebra and the quiver Hecke algebra of the corresponding type via equivariant… read more here.
Keywords: weyl duality; affine schur; quiver type; quantum affine ... See more keywords