Related papers: Recursive algorithm and branching for nonmaximal e…
The decomposition of representations of compact classical Lie groups into representations of finite subgroups is discussed. A Mathematica package is presented that can be used to compute these branching rules using the Weyl character…
The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In addition to encoding finer information on the…
We present the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie Algebras and representation theory, such as tensor product decomposition and subalgebra branching of…
We construct a sequence of Markov processes on the set of dominant weights of an affine Lie algebra $\mathfrak{g}$ considering tensor product of irreducible highest weight modules of $\mathfrak{g}$ and specializations of the characters…
The present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum…
We study intersection numbers of invariant divisors in the toric manifold associated with the fan determined by the collection of Weyl chambers for each root system of classical type and of exceptional type $G_2$. We give a combinatorial…
We define a reduction covariant for the representations a la Vinberg associated to stably graded Lie algebras. We then give an analogue of the LLL algorithm for the odd split special orthogonal group and show how this can be combined with…
Extended affine root systems appear as the root systems of extended affine Lie algebras. A subclass of extended affine root systems, whose elements are called ``minimal" turns out to be of special interest mostly because of the geometric…
Affine Lie algebras admit non-classical highest-weight theories through alternative partitions of the root system. Although significant inroads have been made, much of the classical machinery is inapplicable in this broader context, and…
Splint is a decomposition of root system into union of root systems. Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive subalgebras. Splint can be used to construct branching…
In this paper we continue the study of good re-embeddings of affine K-algebras started in [KLR]. The idea is to use special linear projections to find isomorphisms between a given affine K-algebra K[X]/I, where X=(x_1,...,x_n), and…
We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…
We give faster algorithms for weak expander decompositions and approximate max flow on undirected graphs. First, we show that it is possible to "warm start" the cut-matching game when computing weak expander decompositions, avoiding the…
A numerical algorithm that computes the decomposition of any finite-dimen\-sio\-nal unitary reducible representation of a compact Lie group is presented. The algorithm, which does not rely on an algebraic insight on the group structure, is…
We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…
We study branching problems for affine Kac--Moody algebras. Unlike the finite-dimensional case, an affine Kac--Moody algebra may contain proper subalgebras isomorphic to itself, such as winding subalgebras obtained by rescaling the loop…
A non-iterative method is presented to calculate the closest Wannier functions (CWFs) to a given set of localized guiding functions, such as atomic orbitals, hybrid atomic orbitals, and molecular orbitals, based on minimization of a…
In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra.…
Suppose that W is a finite, unitary, reflection group acting on the complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in W, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a…
We discuss some applications of fusion rules and intertwining operators in the representation theory of cyclic orbifolds of the triplet vertex operator algebra. We prove that the classification of irreducible modules for the orbifold vertex…