Hirota derivatives and representation theory

Hodge Theory and Representation Theory

Hirota Bilinear Formalism and Supersymmetry

Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N = 1 supersymmetric Hirota operators. Using them, we bilinearize SUSY nonlinear evolution equations. The super-soliton solutions and extension to SUSY sine-Gordon are also discussed. As a quite strange paradox it is shown that the Lax integrable SUSY KdV of Manin-Ra...

Hirota Equation and Bethe Ansatz

The paper is a review of recent works devoted to analysis of classical integrable structures in quantum integrable models solved by one or another version of the Bethe ansatz. Similarities between elements of the quantum and classical theories of integrable systems are discussed. Some key notions of the quantum theory, now standard in the quantum inverse scattering method, are identiied with ty...

Representation Theory and Arithmetic

This lecture is a brief introduction to some problems in the contemporary theory of automorphic forms, a part of the spectral theory of group actions, a topic that perhaps began with the theorem of Peter-Weyl on the representation theory of general compact groups; but the clue to the present investigations, and indirectly the major link to Hermann Weyl, is provided by the spectral theory of Har...

Endomorphismalgebras and Representation Theory

Endomorphism algebras gure prominently in group representation theory. F or example, if G is a nite group of Lie type, the representation theory of the endomorphism algebra End G Cj G B |sometimes known as the Hecke algebra over C of G|plays a central role in unraveling the complex unipotent c haracters on G 22, 77. Another example arises in the modular representation theory of the nite general...