Related papers: Harish-Chandra Modules over $\Bbb Z$
Many examples are given of irreducible Harish-Chandra modules for type C having reducible leading term cycles. Examples are also given of irreducibles in category O having reducible associated varieties in type C.
We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite dimensional.…
We give conditions for unitarizability of Harish-Chandra super modules for Lie supergroups and superalgebras.
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…
These are expanded notes from lectures at the Workshop "Representation Theory and Applications" held at Yeditepe University, Istanbul, in honor of Roger E. Howe. They are supplemented by the application of algebraic character theory to the…
It is obtained that an irreducible weight module with finite weight multiplicities over a higher rank Virasoro or super-Virasoro algebra is either a module of the intermediate series, or a so-called finitely-dense module.
Recently the correlation functions of the so-called Itzykson-Zuber/Harish-Chandra integrals were computed (by one of the authors and collaborators) for all classical groups using an integration formula that relates integrals over compact…
The Slodowy slice is an especially nice slice to a given nilpotent conjugacy class in a semisimple Lie algebra. Premet introduced noncommutative quantizaions of the Poisson algebra of polynomial functions on the Slodowy slice. In this…
We continue the study of the fundamental series of generalized Harish-Chandra modules initiated in [PZ2]. Generalized Harish-Chandra modules are (g,k)-modules of finite type where g is a semisimple Lie algebra and k \subset g is a reductive…
We study Harish-Chandra bimodules over the rational Cherednik algebra $H_{c}(W)$ associated to a complex reflection group $W$ with parameter $c$. Our results allow us to partially reduce the study of these bimodules to smaller algebras. We…
We generalize the notion of an intertwining operator to N-graded weak modules over a vertex operator algebra and study their properties. We show a formula for the dimensions of these intertwining operators in terms of modules over the Zhu…
For any irreducible Harish-Chandra module $V$ over the gap-$p$ Virasoro algebra, we determine the condition for $V$ to be unitary.
In this paper, conjugate-linear anti-involutions and unitary Harish-Chandra modules over the Schr\"{o}dinger-Virasoro algebra are studied. It is proved that there are only two classes conjugate-linear anti-involutions over the…
This paper is a review of results on generalized Harish-Chandra modules in the framework of cohomological induction. The main results, obtained during the last 10 years, concern the structure of the fundamental series of…
We apply a new technique based on double affine Hecke algebras to the Harish-Chandra theory of spherical zonal functions. The formulas for the Fourier transforms of the multiplications by the coordinates are obtained as well as a simple…
In the 90's Soergel constructed a functor that relates Harish-Chandra bimodules to Soergel bimodules. We revisit this functor and relate it to the restriction functor constructed by Losev between Harish-Chandra bimodules and bimodules over…
In this paper, we give a new approach to classify all simple Harish-Chandra modules for the N=1 Ramond algebra based on the so called A-cover theory developed in \cite{BF}
Over an arbitrary field of characteristic $\ne 2$, we define the notion of Harish-Chandra pairs, and prove that the category of those pairs is anti-equivalent to the category of algebraic affine supergroup schemes. The result is applied to…
It is shown that there are no simple mixed modules over the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra, which implies that every irreducible weight module over it with a nontrivial finite-dimensional weight space, is a Harish-Chandra…
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.