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Publications Influence

Loop Spaces, Characteristic Classes and Geometric Quantization

- J. Brylinski
- Mathematics
- 1 April 1994

This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Recent developments in mathematical… Expand

759 79

A differential complex for Poisson manifolds

- J. Brylinski
- Mathematics
- 1988

Construction du complexe canonique d'une variete de Poisson. Homologie canonique des varietes symplectiques. Application a l'homologie de Hochschild des algebres non commutatives

353 41

Central extensions of reductive groups by K2

- J. Brylinski, P. Deligné
- Mathematics
- 1 December 2001

108 27- PDF

Universal quantum gates

- J. Brylinski, R. Brylinski
- Physics, Mathematics
- 13 August 2001

In this paper we study universality for quantum gates acting on qudits.Qudits are states in a Hilbert space of dimension d where d is at least two. We determine which 2-qudit gates V have the… Expand

106 14- PDF

Cyclic cohomology of etale groupoids

- J. Brylinski
- Mathematics
- 1 July 1994

We extend Connes’s computation of the cyclic cohomology groups of smooth algebras arising from foliations with separated graphs. We find that the characteristic classes of foliations factor through… Expand

77 14

The geometry of degree-four characteristic classes and of line bundles on loop spaces I

- J. Brylinski, D. Mclaughlin
- Mathematics
- 1 September 1994

104 10

The Spectrum of Certain Invariant Differential Operators Associated to a Hermitian Symmetric Space *

Library of Congress Cataloging In-Publication Data Lie theory and geometry : in honor of Bertram Kostant / Jean-Luc Brylinski... [et al.], editors. p. cm. (Progress in mathematics ; v. 123) Invited… Expand

39 7- PDF

Kazhdan-Lusztig conjecture and holonomic systems

- J. Brylinski, M. Kashiwara
- Mathematics
- 1 October 1981

In [7], D. Kazhdan and G. Lusztig gave a conjecture on the multiplicity of simple modules which appear in a Jordan-H61der series of the Verma modules. This multiplicity is described in the terms of… Expand

329 7- PDF

Lie theory and geometry : in honor of Bertram Kostant

- M. Atiyah, J. Brylinski, R. Brylinski, V. Guillemin, V. Kac
- Mathematics
- 1 July 1997

This volume, dedicated to Kostant on his 65th birthday, is a collection of 22 papers by international leaders in the fields of Lie theory, geometry, algebra and math physics. The papers broadly… Expand

89 7

Differential operators on homogeneous spaces. I

- W. Borho, J. Brylinski
- Mathematics
- 1 October 1982

SummaryIn this paper, we extend recent work of one of us [Br] to investigate an old problem of the other one [B2]. Given a connected semisimple complex Lie-groupG with Lie-algebrag, we study the… Expand

160 4

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