Lectures in Algebraic Combinatorics Young s Construction Seminormal Representations SL 2 Representations Heaps Basics on Finite Fields 1st edition by Adriano M. Garsia, Ömer Eğecioğlu 3030583736 9783030583736

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ISBN-10 :  3030583736 

ISBN-13 :  9783030583736

Author:  Adriano M. Garsia, Ömer Eğecioğlu 

Capturing Adriano Garsia’s unique perspective on essential topics in algebraic combinatorics, this book consists of selected, classic notes on a number of topics based on lectures held at the University of California, San Diego over the past few decades. The topics presented share a common theme of describing interesting interplays between algebraic topics such as representation theory and elegant structures which are sometimes thought of as being outside the purview of classical combinatorics. The lectures reflect Garsia’s inimitable narrative style and his exceptional expository ability. The preface presents the historical viewpoint as well as Garsia’s personal insights into the subject matter. The lectures then start with a clear treatment of Alfred Young’s construction of the irreducible representations of the symmetric group, seminormal representations and Morphy elements. This is followed by an elegant application of SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued fractions and orthogonal polynomials with applications, and finally there is an exposition on the theory of finite fields. The book is aimed at graduate students and researchers in the field.

Lectures in Algebraic Combinatorics Young s Construction Seminormal Representations SL 2 Representations Heaps Basics on Finite Fields 1st table of contents:

1. Alfred Young’s Construction of the Irreducible Representations of S n
2. Young’s Seminormal Representation, Murphy Elements, and Content Evaluations
3. On Finite Dimensional Representations and an Application to Algebraic Combinatorics
4. Heaps, Continued Fractions, and Orthogonal Polynomials
5. Basics on Finite Fields

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Tags: Lectures, Algebraic Combinatorics, Construction Seminormal, Representations, Heaps Basics, Finite Fields, Adriano M. Garsia, Ömer Eğecioğlu