Representation Theory of The $W_{1+\infty}$ Algebra

Details Representation Theory of The $W_{1+\infty}$ Algebra Representation Theory of The $W_{1+\infty}$ Algebra

1994-08-29

arxiv.org/abs/hep-th/9408158v1

Prog.Theor.Phys.Suppl.118:343-374,1995

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, LaTeX, RIMS-990, YITP/K-1087, YITP/U-94-25, SULDP-1994-7

Scientific paper

10.1143/PTPS.118.343

We review the recent development in the representation theory of the $W_{1+\infty}$ algebra. The topics that we concern are, Quasifinite representation, Free field realizations, (Super) Matrix Generalization, Structure of subalgebras such as $W_\infty$ algebra, Determinant formula, Character formula. (Invited talk at ``Quantum Field Theory, Integrable Models and Beyond", YITP, 14-17 February 1994. To appear in Progress of Theoretical Physics Proceedings Supplement.)

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