11,330 research outputs found
A representation theoretic approach to the WZW Verlinde formula
By exploring the description of chiral blocks in terms of co-invariants, a
derivation of the Verlinde formula for WZW models is obtained which is entirely
based on the representation theory of affine Lie algebras. In contrast to
existing proofs of the Verlinde formula, this approach works universally for
all untwisted affine Lie algebras. As a by-product we obtain a homological
interpretation of the Verlinde multiplicities as Euler characteristics of
complexes built from invariant tensors of finite-dimensional simple Lie
algebras. Our results can also be used to compute certain traces of
automorphisms on the spaces of chiral blocks. Our argument is not rigorous; in
its present form this paper will therefore not be submitted for publication.Comment: 37 pages, LaTeX2e. wrong statement in subsection 4.2 corrected and
rest of the paper adapte
Noncommutative localization in topology
A survey of the applications of the noncommutative Cohn localization of rings
to the topology of manifolds with infinite fundamental group, with particular
emphasis on the algebraic K- and L-theory of generalized free products.Comment: 20 pages, LATEX. To appear in the Proceedings of the Conference on
Noncommutative Localization in Algebra and Topology, ICMS, Edinburgh, 29-30
April, 2002. v2 is a minor revision of v
Strong approximation methods in group theory, an LMS/EPSRC Short course lecture notes
These are the lecture notes for the LMS/EPSRC short course on strong
approximation methods in linear groups organized by Dan Segal in Oxford in
September 2007.Comment: v4: Corollary 6.2 corrected, added a few small remark
Commutative Algebras of Ordinary Differential Operators with Matrix Coefficients
A classification of commutative integral domains consisting of ordinary
differential operators with matrix coefficients is established in terms of
morphisms between algebraic curves.Comment: AMS-TeX format, 16 page
Generalized double affine Hecke algebras of higher rank
We define generalized double affine Hecke algebras (GDAHA) of higher rank,
attached to a non-Dynkin star-like graph D. This generalizes GDAHA of rank 1
defined in math.QA/0406480 and math.QA/0409261. If the graph is extended D4,
then GDAHA is the algebra defined by Sahi in q-alg/9710032, which is a
generalization of the Cherednik algebra of type BCn. We prove the formal PBW
theorem for GDAHA, and parametrize its irreducible representations in the case
when D is affine (i.e. extended D4, E6, E7, E8) and q=1. We formulate a series
of conjectures regarding algebraic properties of GDAHA. We expect that,
similarly to how GDAHA of rank 1 provide quantizations of del Pezzo surfaces
(as shown in math.QA/0406480), GDAHA of higher rank provide quantizations of
deformations of Hilbert schemes of these surfaces. The proofs are based on the
study of the rational version of GDAHA (which is closely related to the
algebras studied in math.QA/0401038), and differential equations of
Knizhnik-Zamolodchikov type.Comment: 25 pages, latex; minor corrections are made, some proofs were
expande
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