Zobrazeno 1 - 10
of 341
pro vyhledávání: '"Leclerc, Bernard"'
Publikováno v:
Proc. Lond. Math. Soc. (3) 129 (2024), no. 3, Paper No. e12630
We introduce a family of cluster algebras of infinite rank associated with root systems of type $A$, $D$, $E$. We show that suitable completions of these cluster algebras are isomorphic to the Grothendieck rings of the categories $\mathcal{O}_\mathbb
Externí odkaz:
http://arxiv.org/abs/2401.04616
Autor:
Hernandez, David, Leclerc, Bernard
This article is an extended version of the minicourse given by the second author at the summer school of the conference "Interactions of quantum affine algebras with cluster algebras, current algebras and categorification", held in June 2018 in Washi
Externí odkaz:
http://arxiv.org/abs/1902.01432
Publikováno v:
Math. Z. 295 (2020), no. 3-4, 1245-1277
Let $C$ be a symmetrizable generalized Cartan matrix with symmetrizer $D$ and orientation $\Omega$. In previous work we associated an algebra $H$ to this data, such that the locally free $H$-modules behave in many aspects like representations of a he
Externí odkaz:
http://arxiv.org/abs/1812.09663
Publikováno v:
J. Algebra 558 (2020), 411-422
We show that in case a cluster algebra coincides with its upper cluster algebra and the cluster algebra admits a grading with finite dimensional homogeneous components, the corresponding Berenstein-Zelevinsky quantum cluster algebra can be viewed as
Externí odkaz:
http://arxiv.org/abs/1807.09826
Publikováno v:
Proc. Lond. Math. Soc. (3) 117 (2018), no. 1, 125-148
We generalize the Caldero-Chapoton formula for cluster algebras of finite type to the skew-symmetrizable case. This is done by replacing representation categories of Dynkin quivers by categories of locally free modules over certain Iwanaga-Gorenstein
Externí odkaz:
http://arxiv.org/abs/1704.06438
Publikováno v:
Selecta Math. (N.S.) 24 (2018), no. 4, 3283-3348
We generalize Lusztig's nilpotent varieties, and Kashiwara and Saito's geometric construction of crystal graphs from the symmetric to the symmetrizable case. We also construct semicanonical functions in the convolution algebras of generalized preproj
Externí odkaz:
http://arxiv.org/abs/1702.07570
Autor:
Hernandez, David, Leclerc, Bernard
Publikováno v:
Algebra Number Theory 10 (2016) 2015-2052
Let $\mathcal{O}$ be the category of representations of the Borel subalgebra of a quantum affine algebra introduced by Jimbo and the first author. We show that the Grothendieck ring of a certain monoidal subcategory of $\mathcal{O}$ has the structure
Externí odkaz:
http://arxiv.org/abs/1603.05014
Autor:
Leclerc, Bernard-Simon
Les chutes chez les personnes âgées représentent un problème majeur. Il n’est donc pas étonnant que l’identification des facteurs qui en accroissent le risque ait mobilisé autant d’attention. Les aînés plus fragiles ayant besoin de sout
Externí odkaz:
http://hdl.handle.net/1866/4286
Publikováno v:
Represent. Theory 20 (2016), 375-413
We realize the enveloping algebra of the positive part of a semisimple complex Lie algebra as a convolution algebra of constructible functions on module varieties of some Iwanaga-Gorenstein algebras of dimension 1.
Comment: This article, togethe
Comment: This article, togethe
Externí odkaz:
http://arxiv.org/abs/1511.06216
Publikováno v:
Int. Math. Res. Not. IMRN 2018, no. 9, 2866-2898
For $k \ge 1$ we consider the $K$-algebra $H(k) := H(C,kD,\Omega)$ associated to a symmetrizable Cartan matrix $C$, a symmetrizer $D$, and an orientation $\Omega$ of $C$, which was defined in Part 1. We construct and analyse a reduction functor from
Externí odkaz:
http://arxiv.org/abs/1511.05898