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15
DBranes, RRFields and Duality ON NONCOMMUTATIVE MANIFOLDS
, 2006
"... We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of Tduality as well as establishing a very general formula for Dbrane charges. This formula is closely related to a noncommutative GrothendieckRiemannRoch theorem that is ..."
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Cited by 12 (1 self)
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We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of Tduality as well as establishing a very general formula for Dbrane charges. This formula is closely related to a noncommutative GrothendieckRiemannRoch theorem that is proved here. Our approach relies on a very general form of Poincaré duality, which is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant Ktheory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams.
Complex Structure on the Smooth Dual of GL(n)
 DOCUMENTA MATH.
, 2002
"... Let G denote the padic group GL(n), let Π(G) denote the smooth dual of G, let Π(Ω) denote a Bernstein component of Π(G) and let H(Ω) denote a Bernstein ideal in the Hecke algebra H(G). With the aid of Langlands parameters, we equip Π(Ω) with the structure of complex algebraic variety, and prove tha ..."
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Cited by 7 (3 self)
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Let G denote the padic group GL(n), let Π(G) denote the smooth dual of G, let Π(Ω) denote a Bernstein component of Π(G) and let H(Ω) denote a Bernstein ideal in the Hecke algebra H(G). With the aid of Langlands parameters, we equip Π(Ω) with the structure of complex algebraic variety, and prove that the periodic cyclic homology of H(Ω) is isomorphic to the de Rham cohomology of Π(Ω). We show how the structure of the variety Π(Ω) is related to Xi’s affirmation of a conjecture of Lusztig for GL(n, C). The smooth dual Π(G) admits a deformation retraction onto the tempered dual Π t (G).
Some Fréchet algebras for which the Chern character is an isomorphism
, 2005
"... Abstract. Using similarities between topological Ktheory and periodic cyclic homology we show that, after tensoring with C, for certain Fréchet algebras the Chern character provides an isomorphism between these functors. This is applied to prove that the Hecke algebra and the Schwartz algebra of a ..."
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Cited by 3 (3 self)
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Abstract. Using similarities between topological Ktheory and periodic cyclic homology we show that, after tensoring with C, for certain Fréchet algebras the Chern character provides an isomorphism between these functors. This is applied to prove that the Hecke algebra and the Schwartz algebra of a reductive padic group have isomorphic periodic cyclic homology.
Cyclic homology and pseudodifferential operators, a survey
, 2002
"... We present a brief introduction to Hochschild and cyclic homology designed for researchers interested in pseudodifferential operators and their applications to index theory, spectral invariants, and asymptotics. ..."
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Cited by 2 (2 self)
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We present a brief introduction to Hochschild and cyclic homology designed for researchers interested in pseudodifferential operators and their applications to index theory, spectral invariants, and asymptotics.
Geometric counterpart of the BaumConnes map for GL(n)
"... We describe a geometric counterpart of the BaumConnes map for the padic group GL(n) ..."
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We describe a geometric counterpart of the BaumConnes map for the padic group GL(n)
HOMOLOGICAL ALGEBRA FOR SCHWARTZ ALGEBRAS
"... Abstract. Let G be a reductive group over a nonArchimedean local field. For two tempered smooth representations, it makes no difference for the Extgroups whether we work in the category of tempered smooth representations of G or of all smooth representations of G. Similar results hold for certain ..."
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Abstract. Let G be a reductive group over a nonArchimedean local field. For two tempered smooth representations, it makes no difference for the Extgroups whether we work in the category of tempered smooth representations of G or of all smooth representations of G. Similar results hold for certain discrete groups. We explain the basic ideas from functional analysis and geometric group theory that are needed to state this result correctly and prove it. 1.
Chern character for the Schwartz algebra of padic GL(n)
"... Atiyah has demonstrated that rational cohomology of a compact Hausdorff space can be defined in terms of Ktheory. This is made possible by the existence of a Chern character ..."
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Atiyah has demonstrated that rational cohomology of a compact Hausdorff space can be defined in terms of Ktheory. This is made possible by the existence of a Chern character
ON NONCOMMUTATIVE MANIFOLDS
, 2006
"... Abstract. We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of Tduality as well as establishing a very general formula for Dbrane charges. This formula is closely related to a noncommutative GrothendieckRiemannRoch theore ..."
Abstract
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Abstract. We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of Tduality as well as establishing a very general formula for Dbrane charges. This formula is closely related to a noncommutative GrothendieckRiemannRoch theorem that is proved here. Our approach relies on a very general form of Poincaré duality, which is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant Ktheory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams.
REDUCED C ∗ALGEBRA OF THE pADIC GROUP GL(n) II
, 2001
"... HarishChandra, in his search for the Plancherel measure on a reductive padic group, had a clear conception of the support of the Plancherel measure [13]. The support is a C ∞manifold with countably many connected components. Each component is a compact torus T ..."
Abstract
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HarishChandra, in his search for the Plancherel measure on a reductive padic group, had a clear conception of the support of the Plancherel measure [13]. The support is a C ∞manifold with countably many connected components. Each component is a compact torus T