Twisted K-theory and loop group representations

Abstract

This is the third paper of a series relating the equivariant twisted $K$-theory of a compact Lie group $G$ to the ``Verlinde space'' of isomorphism classes of projective lowest-weight representations of the loop groups. Here, we treat arbitrary compact Lie groups. In addition, we discuss the relation to semi-infinite cohomology, the fusion product of Conformal Field theory, the rôle of energy and the topological Peter-Weyl theorem.

The final SELF-CONTAINED version is v.2. The current version had some material removed to the prequels [FHT1,2]. Minor notational changes

References in corpus (5)

• Twisted K-theory and K-theory of bundle gerbes
• The Verlinde algebra is twisted equivariant K-theory
• Twisted K-theory and loop groups
• K-Theory Past and Present
• A character formula for certain representations of loop groups based on non-simply connected Lie groups

Cited by in corpus (48)

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• The RR charges of A-type Gepner models
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• A Stringy Product on Twisted Orbifold K-theory
• On the Twisted K-Homology of Simple Lie Groups
• Fusion of symmetric $D$-branes and Verlinde rings
• The coset D-branes of SU(n)
• Twisted K-theory, old and new
• D-branes in N=2 coset models and twisted equivariant K-theory
• The differential topology of loop spaces
• K-theoretical boundary rings in N=2 coset models
• A new perspective on the Frenkel-Zhu fusion rule theorem
• The Loop Group of E8 and Targets for Spacetime
• On the Structure of the Fusion Ideal
• A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models
• Thom Prospectra for Loopgroup representations
• Differential Twisted K-theory and Applications
• Charges of twisted branes: the exceptional cases
• Classical Chern-Simons on manifolds with spin structure
• D-Brane Charges in Gepner Models
• Twisted K-theory and finite-dimensional approximation
• Twisted brane charges for non-simply connected groups
• Level-rank duality of untwisted and twisted D-branes
• Level-rank duality of D-branes on the SU(N) group manifold
• K-theory of the moduli of bundles over a Riemann surface and deformations of the Verlinde algebra
• Projective unitary representations of smooth Deligne cohomology groups
• Products and push-forwards in parametrised cohomology theories
• Twisted equivariant K-theory, groupoids and proper actions
• Equivariant K-theory, groupoids and proper actions
• Twisted K-Theory and TQFT
• The ring structure for equivariant twisted K-theory
• An approach toward a finite-dimensional definition of twisted K-theory
• Supersymmetric WZW models and twisted K-theory of SO(3)
• A mathematical formalism for the Kondo effect in WZW branes
• Twisted D-branes of the SU(N)_K WZW model and level-rank duality
• Multiplicative Bundle Gerbes with Connection
• The Classification of Two Dimensional topological Field Theories
• Periodic Cyclic Homology and Equivariant Gerbes
• From gauge anomalies to gerbes and gerbal actions
• Lectures on Noncommutative Geometry
• Dirac Families for Loop Groups as Matrix Factorizations
• The String Topology Loop Coproduct and Cohomology Operations
• Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology
• Twisted representation rings and Dirac induction
• Verlinde modules and quantization