Related papers: WZNW Models from Non-Standard Bilinear Forms

When we describe non-compact or singular Calabi-Yau manifolds by CFT, continuous as well as discrete representations appear in the theory. These representations mix in an intricate way under the modular transformations. In this article, we…

This paper is motivated by several combinatorial actions of the affine Weyl group of type $C_n$. Addressing a question of David Vogan, it was shown in an earlier paper that these permutation representations are essentialy…

For quantized universal enveloping algebras we construct weight modules by inducing representations of the centralizer of the Cartan subalgebra in the quantized universal enveloping algebra. The induced modules arising from…

We prove an integral R = T theorem for odd two dimensional p-adic representations of the absolute Galois group which are unramified at p, extending results of [CG] to the non-minimal case. We prove, for any p, the existence of Katz modular…

C*-algebras generalizing Cuntz-Krieger algebras can be associated to hyperbolic homeomorphisms of compact metric spaces. They satisfy a non-commutative form of Spanier-Whitehead duality with respect to K-theory. We prove this for the case…

Fix an odd prime $p$ and let $f$ be a non-ordinary eigen-cuspform of weight $k$ and level coprime to $p$. Assuming $p>k-1$, we compute asymptotic formulas for the Iwasawa invariants of the Mazur-Tate elements attached to $f$ in terms of the…

This is an introduction to the microscopic techniques of non-rational bulk and boundary conformal field theory which are needed to describe strings moving in non-compact curved backgrounds. The latter arise e.g. in the context of…

Generalizing the super duality formalism for finite-dimensional Lie superalgebras of type $ABCD$, we establish an equivalence between parabolic BGG categories of a Kac-Moody Lie superalgebra and a Kac-Moody Lie algebra. The characters for a…

These lecture notes are a brief introduction to Wess-Zumino-Witten models, and their current algebras, the affine Kac-Moody algebras. After reviewing the general background, we focus on the application of representation theory to the…

In this paper we study the finite W-algebra for the queer Lie superalgebra Q(n) associated with the non-regular even nilpotent coadjoint orbits in the case when the corresponding nilpotent element has Jordan blocks each of size l. We prove…

We consider the standard vector and chiral gauged WZNW models by their gauged maximal null subgroups and show that they can be mapped to each other by a special transformation. We give an explicit expression for the map in the case of the…

For a nondegenerate additive subgroup $G$ of the $n$-dimensional vector space $F^n$ over an algebraically closed field $F$ of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type $W(G,n)$ spanned by all…

Conjunctive normal forms where every clause has length at most two are called 2-CNFs. We study minimally unsatisfiable 2-CNFs (2-MUs), that is, unsatisfiable 2-CNFs where removing any clause destroys unsatisfiability, and obtain their full…

The main result of the paper establishes the irreducibility of a large family of nonzero central charge induced modules over Affine Lie algebras for any non standard parabolic subalgebra. It generalizes all previously known partial results…

We find modular transformations of normalized characters for the following $W$-algebras: (a) $W^{min}_k(\frak{g})$, where $\frak{g}=D_n \, (n \geq 4)$, or $E_6$, $E_7$, $E_8$, and $k$ is a negative integer $\geq -2$, or $\geq…

We introduce a new construction of bilinear invariant forms on Lie algebras, based on the method of graded contractions. The general method is described and the $\Bbb Z_2$-, $\Bbb Z_3$-, and $\Bbb Z_2\otimes\Bbb Z_2$-contractions are found.…

In his famous 2007 paper on three dimensional quantum gravity, Witten defined candidates for the partition functions $$Z_k(q)=\sum_{n=-k}^{\infty}w_k(n)q^n$$ of potential extremal CFTs with central charges of the form $c=24k$. Although such…

We review the description of a particular deformation of the WZW model. The resulting theory exhibits a Poisson-Lie symmetry with a non-Abelian cosymmetry group and can be vectorially gauged.

We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for…

We present a new class of topological conformal field theories (TCFT) characterized by a rational $W$ potential, which includes the minimal models of A and D types as its subclasses. An explicit form of the $W$ potential is found by solving…