相关论文: Localization of modules over small quantum groups

This is an expository lecture, for the Abel bicentennial (Oslo, 2002), describing some recent work on the (small) quantum cohomology ring of Grassmannians and other homogeneous varieties.

Let \(R\) be a commutative ring and \(M\) an \(R\)-module. We develop a localization and local-global theory for \(C4\)-modules, \(C4^{\ast}\)-modules, strongly \(C4^{\ast}\)-modules, \(C4\)-hulls, and pseudo-continuous hulls over…

In this paper, the module algebra structures of $X_{q}(A_{1})$ on quantum polynomial algebra $\C_{q}[x,y,z]$ are investigated, and a complete classification of $X_{q}(A_{1})$-module algebra structures on $\C_{q}[x,y,z]$ is given

The possibilities of unlike particle correlations for a study of particle delays and spatial shifts in relativistic heavy ion collisions are demonstrated. This report represents the unpublished Ref. [4] in the paper by S. Voloshin et al.,…

Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

In this paper, we classify all simple modules over the quantum torus $\mathbb{C}_{\nu}[x^{\pm1},y^{\pm1}]$ and the quantum group $U_q(\mathfrak{sl_2})$ for generic case.

Recent results of the authors on quantum bounded symmetric domains and quantum Harish-Chandra modules are expounded.

Correlations and measures of entanglement in ground state wavefunctions of relativistic quantum field theories are spatially localized over length scales set by the mass of the lightest particle. We utilize this localization to design…

In this paper we study of the BGG-categories $\mathcal O_q$ associated to quantum groups. We prove that many properties of the ordinary BGG-category $\mathcal O$ for a semisimple complex Lie algebra carry over to the quantum case. Of…

In the present paper we discuss some recent versions of localisation methods for calculations in the groups of points of algebraic-like and classical-like groups. Namely, we describe relative localisation, universal localisation, and…

Let $\Oq(G)$ be the algebra of quantized functions on an algebraic group $G$ and $\Oq(B)$ its quotient algebra corresponding to a Borel subgroup $B$ of $G$. We define the category of sheaves on the "quantum flag variety of $G$" to be the…

We report on the development of a modular platform for programmable quantum simulation with atomic quantum gases. The platform is centered around exchangeable optical modules with versatile functionalities. The performance of each module is…

We establish a cluster theoretical interpretation of the isomorphisms of [F.-H.-O.-O., J. Reine Angew. Math., 2022] among quantum Grothendieck rings of representations of quantum loop algebras. Consequently, we obtain a quantization of the…

We describe how some aspects of abstract localization on module categories have applications to the study of injective comodules over some special types of corings. We specialize the general results to the case of Doi-Koppinen modules,…

Matlis duals of local cohomology modules are investigated with respect to many different topics (see section 0 - Introduction). One of these topics are complete intersections - see Corollary 1.1.4.

Our previous work (math.QA/9808015) introduces the basic notions and announces some results on function theory in the quantum disc. The present paper establishes a relationship between those results and the quantum groups theory.

In this paper we use invariant theory to develop the notion of cohomological detection for Type I classical Lie superalgebras. In particular we show that the cohomology with coefficients in an arbitrary module can be detected on smaller…

The Ionization Potentials of small Li_N clusters are calculated with a Shell Correction Method. They are used to illustrate that, within the jellium approximation, deformed cluster shapes provide an adequate description of the observed…

This paper is about $\phi$-coordinated modules for weak quantum vertex algebras. Among the main results, several canonical connections among $\phi$-coordinated modules for different $\phi$ are established. For vertex operator algebras, a…

The contents of this paper has been incorporated into math.CO/0308288.