相关论文: Localization of modules over small quantum groups
In this note we compute length, support and dimension of syzygy modules of certain modules. This partially answers questions asked by Huneke et al.
These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…
We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…
This volume contains a selection of papers presented at the 9th in a series of international conferences on Quantum Simulation and Quantum Walks (QSQW). During this event, we worked on the development of theories based upon quantum walks…
We prove a singular version of Beilinson-Bernstein localization for a complex semi-simple Lie algebra following ideas from the positive characteristic case done by \cite{BMR2}. We apply this theory to translation functors, singular blocks…
This is an expanded version of the third author's lecture in String-Math 2015 at Sanya. It summarizes some of our works in quantum cohomology. After reviewing the quantum Lefschetz and quantum Leray--Hirsch, we discuss their applications to…
This text is the preprint version of the concluding chapter for the book New Directions in Locally Compact Groups published by Cambridge University Press in the series Lecture Notes of the LMS. The recent progress on locally compact groups…
In this talk I summarize the capability of future lepton colliders to discover leptoquarks and to determine their electroweak quantum numbers. This analysis is an updated discussion based on the results presented in the Snowmass 1996 New…
We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously. The full moduli space is found for $\le 3$ points, and a…
A critique to the article by C.A. Fuchs, N.D. Mermin, and R.Schack, "An introduction to QBism with and application to the locality of quantum mechanics" that appeared in Am. J. Phys. 82 (8), 749-754 (2014)
Let $U_q$ be the quantum group corresponding to a complex simple Lie algebra $\mathfrak g$ with root system $R$. Assume the quantum parameter $q\in \C$ is a root of unity. In this paper we study the extensions between simple modules in the…
This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2)…
This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence…
We make comments on Gaidarzhy {\it et al.}'s [{\it Phys. Rev. Lett.} 94, 030402 (2005)] letter.
In this article we discuss Bousfield localization, beginning with definitions in terms of mapping spaces and working up to a discussion of how they can be constructed when we have access to the small object argument. We also discuss…
The Hecke category is at the heart of several fundamental questions in modular representation theory. We emphasise the role of the "philosophy of deformations" both as a conceptual and computational tool, and suggest possible connections to…
The content of this paper is incorporated into hep-th/9805093
This paper is a survey on the representation theory of Hecke algebras, Ariki-Koike algebras and connections with quantum group.
This text is a summary (in french) of recent works in collaboration with Mathieu Lewin, on the modelling of polarons in quantum crystals.
We quantize the coordinate ring of the moduli space of B-bundles on the elliptic curve. Here B is a Borel subgroup of some semisimple Lie group. We construct some representations of these algebras and study intertwining operators for these…