Dualities and Representations of Lie Superalgebras (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 144)

This book provides a comprehensive account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type, serving as an excellent introduction to representation theory of Lie superalgebras.

The author rigorously proves several folklore results, sometimes with new proofs, and presents three important dualities: Schur duality, Howe duality, and super duality.

The book also develops the combinatorics of symmetric functions as needed in connections to Harish-Chandra homomorphism and irreducible characters for Lie superalgebras.

Additionally, the author presents Schur-Sergeev duality for the queer Lie superalgebra from scratch with complete detail, and Howe duality for Lie superalgebras in book form for the first time.

Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras, providing a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.