Related papers: Harish-Chandra Modules over $\Bbb Z$
We establish an isomorphism between the space of logarithmic intertwining operators among suitable generalized modules for a vertex operator algebra and the space of homomorphisms between suitable modules for a generalization of Zhu's…
In this paper we continue the study of the category of modular Harish-Chandra bimodules initiated by Bezrukavnikov and Riche and also study the modular version of the BGG category $\mathcal{O}$. We prove a version of the…
We prove that any irreducible Harish-Chandra modules for a class of Lie algebras, which we call gap-$p$ Virasoro algebras, must be a highest weight module, a lowest weight module, or a module of intermediate series.These algebras are…
In this note we introduce and investigate the concepts of dual entwining structures and dual entwined modules. This generalizes the concepts of dual Doi-Koppinen structures and dual Doi-Koppinen modules introduced (in the infinite case over…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
The purpose of this paper is to generalize Zhu's theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights.…
We obtain a classification of simple modules with finite weight multiplicities over basic classical map superalgebras. Any such module is parabolic induced from a simple cuspidal bounded module over a cuspidal map superalgebra. Further on,…
We classify all simple strong Harish-Chandra modules for the Lie superalgebra $W(m,n)$. We show that every such module is either strongly cuspidal or a module of the highest weight type. We construct tensor modules for $W(m,n)$, which are…
For any complex parameters a,b, the W(a,b) algebra is the Lie algebra with basis {L_i,W_i|i\in Z}, and relations [L_i,L_j]=(j-i)L_{i+j}, [L_i,W_j]=(a+j+bi)W_{i+j},[W_i,W_j]=0. In this paper, indecomposable modules of the intermediate series…
The two papers in this series analyze quantum invariant differential operators for quantum symmetric spaces in the maximally split case. In this paper, we complete the proof of a quantum version of Harish-Chandra's theorem: There is a…
We analyze the centralizer of the Macdonald difference operator in an appropriate algebra of Weyl group invariant difference operators. We show that it coincides with Cherednik's commuting algebra of difference operators via an analog of…
In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…
We define an affine Jacquet functor and use it to describe the structure of induced affine Harish-Chandra modules at noncritical levels, extending the theorem of Kac and Kazhdan [KK] on the structure of Verma modules in the…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
Dunkl operators associated with finite reflection groups generate a commutative algebra of differential-difference operators. There exists a unique linear operator called intertwining operator which intertwines between this algebra and the…
The $H$-ring structure of certain infinite(-dimensional) Grassmannians is discussed using various algebraic and analytical methods but so that cellular arguments are avoided. These methods allow us to discuss these Grassmannian in greater…
A well-known theorem of Mathieu's states that a Harish-chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous…
This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with…
In this paper we study the category of Harish-Chandra bimodules $HC_{\chi,\psi}$ in the Deligne category $\text{Rep}(GL_t)$. In particular, we answer Question 3.25 posed in Pavel Etingof's paper arXiv:1407.0373 and determine for which…
In this paper we study the structure of completions of symplectic reflection algebras. Our results provides a reduction to smaller algebras. We apply this reduction to the study of two-sided ideals and Harish-Chandra bimodules.