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Author :
Release : 2006
Genre : Orthogonal polynomials
Kind : eBook
Book Rating : 472/5 ( reviews)
Book Synopsis Jack, Hall-Littlewood and Macdonald Polynomials by :
Download or read book Jack, Hall-Littlewood and Macdonald Polynomials written by . This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vadim B. Kuznetsov
Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 838/5 ( reviews)
Book Synopsis Jack, Hall-Littlewood and Macdonald Polynomials by : Vadim B. Kuznetsov
Download or read book Jack, Hall-Littlewood and Macdonald Polynomials written by Vadim B. Kuznetsov. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt: The subject of symmetric functions began with the work of Jacobi, Schur, Weyl, Young and others on the Schur polynomials. In the 1950's and 60's, far-reaching generalizations of Schur polynomials were obtained by Hall and Littlewood (independently) and, in a different direction, by Jack. In the 1980's, Macdonald unified these developments by introducing a family of polynomials associated with arbitrary root systems. The last twenty years have witnessed considerable progress in this area, revealing new and profound connections with representation theory, algebraic geometry, combinatorics, special functions, classical analysis and mathematical physics. All these fields and more are represented in this volume, which contains the proceedings of a conference on Jack, Hall-Littlewood and Macdonald polynomials held at ICMS, Edinburgh, during September 23-26, 2003. of historical material, including brief biographies of Hall, Littlewood, Jack and Macdonald; the original papers of Littlewood and Jack; notes on Hall's work by Macdonald; and a recently discovered unpublished manuscript by Jack (annotated by Macdonald). The book will be invaluable to students and researchers who wish to learn about this beautiful and exciting subject.
Author : Masatoshi Noumi
Release :
Genre :
Kind : eBook
Book Rating : 879/5 ( reviews)
Book Synopsis Macdonald Polynomials by : Masatoshi Noumi
Download or read book Macdonald Polynomials written by Masatoshi Noumi. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:
Author : James Haglund
Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 113/5 ( reviews)
Book Synopsis The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics by : James Haglund
Download or read book The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics written by James Haglund. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.
Author : Yusra Fatima Naqvi
Release : 2014
Genre : Polynomials
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis A Product Formula for Certain Littlewood-Richardson Coefficients for Jack and Macdonald Polynomials by : Yusra Fatima Naqvi
Download or read book A Product Formula for Certain Littlewood-Richardson Coefficients for Jack and Macdonald Polynomials written by Yusra Fatima Naqvi. This book was released on 2014. Available in PDF, EPUB and Kindle. Book excerpt: Jack polynomials generalize several classical families of symmetric polynomials, including Schur polynomials, and are further generalized by Macdonald polynomials. In 1989, Richard Stanley conjectured that if the Littlewood-Richardson coefficient for a triple of Schur polynomials is 1, then the corresponding coefficient for Jack polynomials can be expressed as a product of weighted hooks of the Young diagrams associated to the partitions indexing the coefficient. We prove a special case of this conjecture in which the partitions indexing the Littlewood-Richardson coefficient have at most 3 parts. We also show that this result extends to Macdonald polynomials.
