Algebraic combinatorics has evolved into one of the most active areas of mathematics during the last several decades. Its recent developments have become more interactive with not only its traditional field representation theory but also algebraic geometry, harmonic analysis and mathematical physics.This book presents articles from some of the key contributors in the area. It covers Hecke algebras, Hall algebras, the Macdonald polynomial and its deviations, and their relations with other fields.
* Uno's Conjecture on Representation Types of Hecke Algebras (S Ariki) * Quiver Varieties, Afine Lie Algebras, Algebras of BPS States, and Semicanonical Basis (I Frenkel et al.) * Divided Differences of Type D and the Grassmannian of Complex Structures (H Duan & P Pragacz) * Tableaux Statistics For Two Part Macdonald Polynomials (L Lapointe & J Morse) * A Crystal to Rigged Configuration Bijection for Nonexceptional Affine Algebras (M Okado et al.) * Littlewood's Formulas for Characters of Orthogonal and Symplectic Groups (A Lascoux) * A q-Analog of Schur's Q-Functions (G Tudose & M Zabrocki)