By V Kac

This e-book is a set of a chain of lectures given via Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. those lectures specialize in the assumption of a maximum weight illustration, which works via 4 assorted incarnationsThe first is the canonical commutation family members of the infinite-dimensional Heisenberg Algebra (= oscillator algebra). the second one is the top weight representations of the Lie algebra gl? of limitless matrices, besides their functions to the speculation of soliton equations, came across by way of Sato and Date, Jimbo, Kashiwara and Miwa. The 3rd is the unitary optimum weight representations of the present (= affine Kac-Moody) algebras. those algebras look within the lectures two times, within the aid conception of soliton equations (Kp ? KdV) and within the Sugawara building because the major instrument within the research of the fourth incarnation of the most notion, the idea of the top weight representations of the Virasoro algebra. . This e-book could be very valuable for either mathematicians and physicists. To mathematicians, it illustrates the interplay of the foremost rules of the illustration concept of infinite-dimensional Lie algebras; and to physicists, this concept is popping into a big portion of such domain names of theoretical physics as soliton thought, concept of two-dimensional statistical versions, and string conception.

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