6,908 research outputs found
Unitary representations of nilpotent super Lie groups
We show that irreducible unitary representations of nilpotent super Lie
groups can be obtained by induction from a distinguished class of sub super Lie
groups. These sub super Lie groups are natural analogues of polarizing
subgroups that appear in classical Kirillov theory. We obtain a concrete
geometric parametrization of irreducible unitary representations by nonnegative
definite coadjoint orbits. As an application, we prove an analytic
generalization of the Stone-von Neumann theorem for Heisenberg-Clifford super
Lie groups
Microlocal KZ functors and rational Cherednik algebras
Following the work of Kashiwara-Rouquier and Gan-Ginzburg, we define a family
of exact functors from category for the rational Cherednik algebra
in type to representations of certain "coloured braid groups" and calculate
the dimensions of the representations thus obtained from standard modules. To
show that our constructions also make sense in a more general context, we also
briefly study the case of the rational Cherednik algebra corresponding to
complex reflection group .Comment: Revised to improve exposition, giving more details on the
construction of the microlocal local systems and providing background
information on twisted D-modules in an appendi
Realizations of Real Low-Dimensional Lie Algebras
Using a new powerful technique based on the notion of megaideal, we construct
a complete set of inequivalent realizations of real Lie algebras of dimension
no greater than four in vector fields on a space of an arbitrary (finite)
number of variables. Our classification amends and essentially generalizes
earlier works on the subject.
Known results on classification of low-dimensional real Lie algebras, their
automorphisms, differentiations, ideals, subalgebras and realizations are
reviewed.Comment: LaTeX2e, 39 pages. Essentially exetended version. Misprints in
Appendix are correcte
Equivariant local cyclic homology and the equivariant Chern-Connes character
We define and study equivariant analytic and local cyclic homology for smooth
actions of totally disconnected groups on bornological algebras. Our approach
contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki
and Lesniewski as a special case and provides an equivariant extension of the
local cyclic theory developped by Puschnigg. As a main result we construct a
multiplicative Chern-Connes character for equivariant KK-theory with values in
equivariant local cyclic homology.Comment: 38 page
A Physical Origin for Singular Support Conditions in Geometric Langlands Theory
We explain how the nilpotent singular support condition introduced into the
geometric Langlands conjecture by Arinkin and Gaitsgory arises naturally from
the point of view of N = 4 supersymmetric gauge theory. We define what it means
in topological quantum field theory to restrict a category of boundary
conditions to the full subcategory of objects compatible with a fixed choice of
vacuum, both in functorial field theory and in the language of factorization
algebras. For B-twisted N = 4 gauge theory with gauge group G, the moduli space
of vacua is equivalent to h*/W , and the nilpotent singular support condition
arises by restricting to the vacuum 0 in h*/W. We then investigate the
categories obtained by restricting to points in larger strata, and conjecture
that these categories are equivalent to the geometric Langlands categories with
gauge symmetry broken to a Levi subgroup, and furthermore that by assembling
such for the groups GL_n for all positive integers n one finds a hidden
factorization structure for the geometric Langlands theory.Comment: 55 pages, 5 figures, more improvements to the expositio
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