Related papers: Maximaland Primitive Elements in Baby Verma Module…
Given $r \in \mathbf{N},$ let $\lambda$ be a partition of $r$ with at most two parts. Let $\mathbf{F}$ be a field of characteristic 3. Write $M^\lambda$ for the $\mathbf{F}S_r$-permutation module corresponding to the action of the symmetric…
We consider principal subspaces $W_{L(k\Lambda_0)}$ and $W_{N(k\Lambda_0)}$ of standard module $L(k\Lambda_0)$ and generalized Verma module $N(k\Lambda_0)$ at level $k\geq 1$ for affine Lie algebra of type $B_2^{(1)}$. By using the theory…
A widely accepted viewpoint is to consider candidates for cosmological dark matter as neutral and weakly interacting particles, as well as to consider only light elements in the pregalactic chemical composition. It is shown that stable…
In the present paper we continue the project of systematic classification and construction of invariant differential operators for non-compact semisimple Lie groups. This time we make the stress on one of the main building blocks, namely…
This is the author's diploma thesis. In the first part of the thesis the algebra structure on the Ext-spaces Ext^k(M(x), M(y)) of Verma modules M(x) and M(y) in the parabolic category O for the case of the parabolic subalgebras gl(n) x…
We study the subvariety of integrable 1-forms in a finite dimensional vector space $W \subset \Omega^1(\mathbb C^n,0)$. We prove that the irreducible components with dimension comparable with the rank of $W$ are of minimal degree.
We study properties of relative modular categories and derive sufficient conditions for their existence. In particular, we derive sufficient conditions for relative pre-modular categories to be non-degenerate and relative modular, and for…
We determine the splitting type of the Verlinde vector bundles in higher genus in terms of simple semihomogeneous factors. In agreement with strange duality, the simple factors are interchanged by the Fourier-Mukai transform, and their…
According to the Ringel-Green Theorem([G],[R1]), the generic composition algebra of the Hall algebra provides a realization of the positive part of the quantum group. Furthermore, its Drinfeld double can be identified with the whole quantum…
The purpose of the paper is to derive formulas that describe the structure of the induced supermodule H^0_G(\la) for the general linear supergroup G=GL(m|n) over an algebraically closed field K of characteristic p\neq 2. Using these…
In 2005, M. Behboodi introduced the notion of a classical prime ring module, which he showed is, in general, nonequivalent to a (Dauns) prime ring module. In this paper, we extended the idea of classical primeness to near-ring module.…
Computing the extensions between Verma modules is in general a very difficult problem. Using Soergel bimodules, one can construct a graded version of the principal block of Category $\mathcal{O}$ for any finite coxeter group. In this…
A new method for direct evaluation of both crystalline structure, bulk modulus B_0, and bulk-modulus pressure derivative B'_0 of solid materials with complex crystal structures is presented. The explicit and exact results presented here…
We observe that a sharp result on the exponential growth rate of the number of primitive elements exists for the free group on two generators.
We study two types of nestings of balanced incomplete block designs (BIBDs). In both types of nesting, we wish to add a point (the nested point) to every block of a $(v,k,\lambda)$-BIBD in such a way that we end up with a partial…
We give skein theoretic formulas for minimal idempotents in the Birman-Murakami-Wenzl algebras. These formulas are then applied to derive various known results needed in the construction of quantum invariants and modular categories. In…
Highest weight modules of the double affine Lie algebra $\widehat{\widehat{\mathfrak{sl}}}_{2}$ are studied under a new triangular decomposition. Singular vectors of Verma modules are determined using a similar condition with horizontal…
We construct a tight-binding model realizing one pair of Weyl nodes and three distinct Weyl semimetals. In the type-I (type-II) Weyl semimetal, both nodes belong to type-I (type-II) Weyl nodes. In addition, there exists a novel type, dubbed…
We present a conceptual overview of a new substructure model of elementary particles, motivated in part by the Gell-Mann-Nishijima formula. In this approach, Weyl spinors endowed with proto-charges generate all known elementary fermions via…
Weyl fermions play a major role in quantum field theory but have been quite elusive as fundamental particles. Materials based on quasi two-dimensional bismuth layers were recently designed and provide an arena for the study of the interplay…