Multiplets of representations and Kostant's Dirac operator for equal rank loop groups

DOI10.1215/S0012-7094-01-11014-4zbMath1018.17016arXivmath/0005057MaRDI QIDQ1847871

Gregory D. Landweber

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0005057

zbMATH Keywords

Dirac operatorloop groupWeyl character formulamultiplet

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Loop groups and related constructions, group-theoretic treatment (22E67) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Semisimple Lie groups and their representations (22E46) Index theory and related fixed-point theorems on manifolds (58J20)

Related Items

Projective families of Dirac operators on a Banach Lie groupoid ⋮ Dirac operators on quasi-Hamiltonian \(G\)-spaces ⋮ Representation rings of Lie superalgebras ⋮ \(K\)-theoretical boundary rings in \(N=2\) coset models ⋮ \(LT\)-equivariant index from the viewpoint of \(KK\)-theory. A global analysis on the infinite-dimensional Heisenberg group ⋮ Dirac induction for loop groups ⋮ Loop groups and twisted \(K\)-theory. III ⋮ Dirac operators on quadratic Lie superalgebras ⋮ A \(K\)-homological approach to the quantization commutes with reduction problem ⋮ Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting ⋮ Loop groups and twisted $K$-theory II ⋮ Twisted representation rings and Dirac induction ⋮ Fractional loop group and twisted \(K\)-theory ⋮ Dirac families for loop groups as matrix factorizations

Cites Work

• Unnamed Item
• Unnamed Item
• Orientation and string structures on loop space
• Superconformal current algebras and their unitary representations
• Symplectic reduction, BRS cohomology, and infinite-dimensional Clifford algebras
• The non-commutative Weil algebra
• A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups
• Lie algebra cohomology and the generalized Borel-Weil theorem
• The Dirac Operator on Homogeneous Spaces and Representations of Reductive Lie Groups I
• The Weyl character formula, the half-spin representations, and equal rank subgroups
• Dirac Operators on a Compact Lie Group