Related papers: Dirac Index and Twisted Characters

Motivated by the maximal subgroup problem of the finite classical groups we begin the classification of imprimitive irreducible modules of finite quasisimple groups. We obtain our strongest results for modules over fields of characteristic…

We study the behavior of Dirac cohomology under Howe's $\Theta$-correspondence in the case of complex reductive dual pairs. More precisely, if $(G_1,G_2)$ is a complex reductive dual pair with $G_1$ and $G_2$ viewed as real groups, we…

We give an index formula for a class of Dirac operators coupled with unbounded potentials. More precisely, we study operators of the form P := D+ V, where D is a Dirac operators and V is an unbounded potential at infinity on a possibly…

We give a cohomological treatment of a character theory for (g,K)-modules. This leads to a nice formalism extending to large categories of not necessarily admissible (g,K)-modules. Due to results of Hecht, Schmid and Vogan the classical…

Starting from an even definite lattice, we construct a principal circle bundle covered by a certain three-step nilpotent Lie group G. On the base space, which is again a nilmanifold, we then study the Dirac operator twisted by the…

We prove that the order of a finite group $G$ with trivial solvable radical is bounded above in terms of ${\rm acd}(G)$, the average degree of the irreducible characters. It is not true that the index of the Fitting subgroup is bounded…

Twisted spectral triples are a twisting of the notion of spectral triple aiming at dealing with some type III geometric situations. In the first part of the paper, we give a geometric construction of the index map of a twisted spectral…

We use enhanced Langlands parameters to obtain a classification for irreducible representations of twisted $p$-adic general linear groups in unramified principal series. We give the definition of standard representations and prove the…

Let $G$ be a non-compact connected semisimple real Lie group with finite center. Suppose $L$ is a non-compact connected closed subgroup of $G$ acting transitively on a symmetric space $G/H$ such that $L\cap H$ is compact. We study the…

In this article a general framework for studying analytic representations of a real Lie group G is introduced. Fundamental topological properties of the representations are analyzed. A notion of temperedness for analytic representations is…

We extend the geometric approach to vertex algebras developed by the first author to twisted modules, allowing us to treat orbifold models in conformal field theory. Let $V$ be a vertex algebra, $H$ a finite group of automorphisms of $V$,…

Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called twisted logarithmic module, involves the…

Let $\G$ be a locally compact group satisfying some technical requirements and $\wG$ its unitary dual. Using the theory of twisted crossed product $C^*$-algebras, we develop a twisted global quantization for symbols defined on $\G\times\wG$…

We extend the Howlett-Isaacs theorem on the solvability of groups of central type taking into account actions by automorphisms. Then we study certain induced characters whose constituents have all the same degree.

For any reductive Lie algebra $\mathfrak{g}$ and commutative, associative, unital algebra $S$, we give a complete classification of the simple weight modules of $\mathfrak{g}\otimes S $ with finite weight multiplicities. In particular, any…

This is a companion article to my papers on Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebras gl(m|n) (much revised!) and q(n). The goal is to develop the general theory of tilting modules for Lie superalgebras,…

We identify the category of integrable lowest-weight representations of the loop group LG of a compact Lie group G with the linear category of twisted, conjugation-equivariant curved Fredholm complexes on the group G: namely, the twisted,…

This is the second in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the "Verlinde ring" of its loop group. We introduce the Dirac family of Fredholm operators…

We introduce the concept of an extension of a semilattice of groups $A$ by a group $G$ and describe all the extensions of this type which are equivalent to the crossed products $A*_\Theta G$ by twisted partial actions $\Theta$ of $G$ on…

In this paper, we introduce the generalised Knutson Index and compute it for the special linear groups and projective special linear groups of degree two by computing the lowest common multiple of the degrees of their irreducible…