相关论文: Bosonic formulas for $\hat{sl_2}$ coinvariants
A bosonic-fermionic correspondence allows an analytic definition of functional super derivative, in particular, and a bosonic functional calculus, in general, on Bargmann- Gelfand triples for the second super quantization. A Feynman…
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special…
We study differential calculus on h-deformed bosonic and fermionic quantum space. It is shown that the fermionic quantum space involves a parafermionic variable as well as a classical fermionic one. Further we construct the classical…
The canonical components of SL_2-character varieties of arithmetic two bridge link groups are determined.
Given any representation of an arbitrary Lie algebra L over a field k of characteristic 0, we construct representations of L on bosonic and fermionic Fock space. The method gives an explicit formula for a (sometimes trivial) 2-cocycle in…
We investigate induced modules of doublet algebra in (1,p) logarithmic models. We give fermionic formulas for the characters of induced modules and coinvariants with respect to different subalgebras calculated in the irreducible modules.…
This is the first of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. For a flat 2--connection, we define the 2-holonomy of…
We provide generating functions for the perturbative massive string spectrum which are covariant with respect to the SO(9) little group, and which contain all the representation theoretic content of the spectrum. Generating functions for…
In this article, various approaches to calculate covariant expressions for the bilinears of Dirac spinors are presented. For this purpose, algebraic equations defining Dirac spinors are discussed. Following that, a covariant approach for…
The algebra of holomorphic polynomial Sp_{2n}-invariants of k complex 2n by 2n matrices (under diagonal conjugation action) is generated by the traces of words in these matrices and their symplectic adjoints. No concrete minimal generating…
Quantum invariants like the colored Jones polynomial are algebraic in nature but are conjectured to detect important information about the geometry of links. In this thesis we explore these connections using an enhanced version of the RT…
We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear,…
We study a class of representations of the Lie algebra of Laurent polynomials with values in the nilpotent subalgebra of sl(3). We derive Weyl-type (bosonic) character formulas for these representations. We establish a connection between…
In this note we give a new construction of the N=2 superconformal algebra using currents of the affine superalgebra $\hat{sl}(2 | 1)$ and free bosonic fields, and also the N=4 superconformal algebra without central charge in terms of…
We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.
Explicit formulas for computation of the Poincar\'e series for the algebras of joint $SL_2$-invariants and covariants of $n$ linear forms in terms of Narayana polynomials are found. Also, for these algebras we calculate the degrees and…
In this text, We compute the equivariant cohomology of Bott-Samelson varieties. Thanks to this computation, we give a new demonstration for the formulas proved by Sarah Billey for the equivariant cohomology of Schubert varieties.
We construct a Hennings type logarithmic invariant for restricted quantum $\mathfrak{sl}(2)$ at a $2\mathsf{p}$-th root of unity. This quantum group $U$ is not braided, but factorizable. The invariant is defined for a pair: a 3-manifold $M$…
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
Deformation quantization of bosonic strings is considered. We show that the light-cone gauge is the most convenient classical description to perform the quantization of bosonic strings in the deformation quantization formalism. Similar to…