Orbits and representation of Krichever-Novikov affine-type algebras

DOI10.1007/BF02362645zbMath0890.17026WikidataQ125761193 ScholiaQ125761193MaRDI QIDQ1356304

Oleg K. Sheinman

Publication date: 8 December 1997

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

zbMATH Keywords

Kac-Moody algebrascentral extensionshighest weight modulesaffine algebrasalmost graded algebrasKrichever-Novikov algebrasWeyl-Kac character formulacoadjoint orbit method

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) 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) Riemann surfaces; Weierstrass points; gap sequences (14H55) Differentials on Riemann surfaces (30F30)

Cites Work

• Orbital theory for affine Lie algebras
• Nonlinear equations and elliptic curves
• Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons
• Virasoro-type algebras, Riemann surfaces and strings in Minkowski space
• Unitary representations of some infinite dimensional groups
• Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
• Representations of the Heisenberg algebra on a Riemann surface
• Algebras of Virasoro type, energy-momentum tensor, and decomposition operators on Riemann surfaces
• Modules with highest weight for affine Lie algebras on Riemann surfaces
• Structure of representations generated by vectors of highest weight

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