Publications of the Research Institute for Mathematical Sciences

Filtered Rings, Filtered Blowing-Ups and Normal Two-Dimensional Singularities with “Star-Shaped” Resolution

Masataka Tomari, Kei-ichi Watanabe

1989 年 25 巻 5 号 p. 681-740
発行日: 1989年
公開日: 2009/01/22

DOIhttps://doi.org/10.2977/prims/1195172704

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Spin Module Versions of Weyl's Reciprocity Theorem for Classical Kac-Moody Lie Algebras —An Application to Branching Rule Duality—

Koji Hasegawa

1989 年 25 巻 5 号 p. 741-828
発行日: 1989年
公開日: 2009/01/22

DOIhttps://doi.org/10.2977/prims/1195172705

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We study tensor products of the spin modules (i.e. the Fermion Fock space representations) for classical (simple or affine) Kac-Moody Lie algebras. We find out that there are mutually commutant pairs of classical Kac-Moody algebras acting on the spin modules, and describe the irreducible decompositions in terms of Young diagrams. As applications, we obtain a simple explanation of Jimbo-Miwa's branching rule duality (i.e. isomorphisms between coset Virasoro modules) [JM], generalization thereof and the duality of the modular transformation rules of affine Lie algebra characters.

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The Super-Toda Lattice Hierarchy

Kaoru Ikeda

1989 年 25 巻 5 号 p. 829-845
発行日: 1989年
公開日: 2009/04/24

DOIhttps://doi.org/10.2977/prims/1195172706

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The super-Toda lattice (STL) hierarchy is introduced. The equivalence between the Lax representation and Zakharov-Shabat representation of the STL hierarchy is shown. Introducing the Lie superalgebra osp(∞|∞), the ortho-symplectic (OSp)-STL hierarchy is defined as well. These equations are solved through the Riemann-Hilbert decomposition of corresponding infinite dimensional Lie supergroups. An explicit representation of solutions is given by means of the super-τ field.

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