相关论文: Gr\"obner bases for fusion products

We give a complete description of the graded multiplicity space which appears in the Feigin-Loktev fusion product [FL99] of graded Kirillov-Reshetikhin modules for all simple Lie algebras. This construction is used to obtain an upper bound…

Fusion of positive energy representations is defined using Connes' tensor product for bimodules over a von Neumann algebra. Fusion is computed using the analytic theory of primary fields and explicit solutions of the Knizhnik-Zamolodchikov…

We give a formula for the relative Deligne tensor product of two indecomposable finite semisimple module categories over a pointed braided fusion category over an algebraically closed field.

In this article, we show in the ADE case that the fusion product of Kirillov-Reshetikhin modules for a current algebra, whose character is expressed in terms of fermionic forms, can be constructed from one-dimensional modules by using…

Let $\mathcal{A}$ be a cluster algebra of finite cluster type. We study the Gr\"obner cone $\mathcal{C}_{\mathcal{A}}$ parametrizing term orders inducing an initial degeneration of the ideal $I_{\mathcal{A}}$ of relations among the cluster…

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…

Let g denote a Lie algebra, and let T(g) denote the tensor product of g with a ring of truncated polynomials. The Lie algebra T(g) is called a truncated current Lie algebra. The highest-weight representation theory of T(g) is developed, and…

We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them…

We analyse the fusion products of certain representations of the Virasoro algebra for c=-2 and c=-7 which are not completely reducible. We introduce a new algorithm which allows us to study the fusion product level by level, and we use this…

We introduce a class of induced representations of the degenerate double affine Hecke algebra of gl_N and analyze their structure mainly by means of intertwiners. We also construct them from modules of the affine Lie algebra using…

We develop the representation theory of shifted quantum affine algebras $\mathcal{U}_q^\mu(\hat{\mathfrak{g}})$ and of their truncations which appeared in the study of quantized K-theoretic Coulomb branches of 3d $N = 4$ SUSY quiver gauge…

We exhibit in this article a contraction of the direct product Lie algebra $g\oplus g$ of a finite-dimensional complex Lie algebra $g$ onto the semi-direct product Lie algebra $g\rtimes g$, where the first factor $g$ is viewed as a trivial…

We derive fusion rules for the composition of $q$-deformed classical representations (arising in tensor products of the fundamental representation) with semi-periodic representations of $SL(N)_q$ at roots of unity. We obtain full…

The theory of unified product and extending structures for alternative and pre-alternative algebras are developed. It is proved that the extending structures of these algebras can be classified by using some non-abelian cohomology and…

We settle the fusion product decomposition theorem for higher-level affine Demazure modules for the cases $E^{(1)}_{6, 7, 8}, F^{(1)}_4$ and $E^{(2)}_{6}$, thus completing the main theorems of Chari et al. (J. Algebra, 2016) and Kus et al.…

We study the category of finite--dimensional representations for a basic classical Lie superalgebra $\Lg=\Lg_0\oplus \Lg_1$. For the ortho--symplectic Lie superalgebra $\Lg=\mathfrak{osp}(1,2n)$ we show that certain objects in that category…

We consider linear star products on $R^d$ of Lie algebra type. First we derive the closed formula for the polydifferential representation of the corresponding Lie algebra generators. Using this representation we define the Weyl star product…

This paper explains the relation between the fusion product of symmetric power sl(n) evaluation modules, as defined by Feigin and Loktev, and the graded coordinate ring R(mu), which describes the cohomology ring of the flag variety Fl(mu)…

The periodic Temperley-Lieb category consists of connectivity diagrams drawn on a ring with $N$ and $N'$ nodes on the outer and inner boundary, respectively. We consider families of modules, namely sequences of modules $\mathsf{M}(N)$ over…

We study Demazure modules which occur in a level $\ell$ irreducible integrable representation of an affine Lie algebra. We also assume that they are stable under the action of the standard maximal parabolic subalgebra of the affine Lie…