Related papers: Fusion in the W_3 algebra
In this note we study simple modules for a reduced enveloping algebra U_chi(g) in the critical case when chi element of g^* is ``nilpotent''. Some dimension formulas computed by Jantzen suggest modified versions of Weyl's dimension formula,…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
We show that the coefficients of decomposition into an irreducible components of the tensor powers of level $r$ symmetric algebra of adjoint representation coincide with the Verlinder numbers. Also we construct (for $sl(2)) the…
In this paper we provide an algebraic derivation of the explicit Witten volume formulas for a few semi-simple Lie algebras by combining a combinatorial method with the ideas used by Gunnells and Sczech in computation of higher-dimensional…
We establish two versions of the fusion procedure for the walled Brauer algebras. In each of them, a complete system of primitive pairwise orthogonal idempotents for the walled Hecke algebra is constructed by consecutive evaluations of a…
In this paper we give two general formulae for the M\"uger centralizers in the category of representations of a semisimple quasitriangular Hopf algebra. The first formula is given in the terms of the Drinfeld map associated to the…
We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain…
We review the main topics concerning Fusion Rule Algebras (FRA) of Rational Conformal Field Theories. After an exposition of their general properties, we examine known results on the complete classification for low number of fields ($\leq…
We survey a number of results regarding the representation theory of $W$-algebras and their connection with the resent development of the four dimensional $N=2$ superconformal field theories in physics.
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
We introduce the tools of intersection theory to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis. In order to illustrate this technique, we consider the Baikov representation of maximal cuts…
We give explicit formulae for certain elements occurring in the Bernstein presentation of an affine Hecke algebra, in terms of the usual Iwahori- Matsumoto generators. We utilize certain minimal expressions for said elements and we give a…
We prove that the Fourier matrices for the imprimitive complex reflection groups introduced by Malle define fusion algebras with not necessarily positive but integer structure constants. Hence they define Z-algebras. As a result, we obtain…
For any normal commutative Hopf subalgebra $K=k^G$ of a semisimple Hopf algebra we describe the ring inside $kG$ obtained by the restriction of $H$-modules. If $G=\Z_p$ this ring determines a fusion ring and we give a complete description…
We explicitly demonstrate that the unitary representations of the $w_\infty$ algebra and its truncations are just the unitary representations of the Virasoro algebra.
We explicitly compute certain Douglas algebras that are invariant under both the Bourgain map and the minimal envelope map. We also compute the Bourgain algebra and the minimal envelope of the maximal subalgebras of a certain singly…
We continue our study of minimal affinizations for algebras of type D, E.
We prove some results on the structure of certain classes of integral fusion categories and semisimple Hopf algebras under restrictions on the set of its irreducible degrees.
The Virasoro logarithmic minimal models were intensively studied by several groups over the last ten years with much attention paid to the fusion rules and the structures of the indecomposable representations that fusion generates. The…
The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…