Год выпуска: 2012 Автор: Lipika Deka Издательство: LAP Lambert Academic Publishing Страниц: 184 ISBN: 9783846584842
Описание
The problem of finding fermionic formulas for the many generalizations of Kostka polynomials and for the characters of conformal field theories has been a very exciting research topic for the last few decades. In this book, which is a dissertation we present new fermionic formulas for the unrestricted Kostka polynomials extending the work of Kirillov and Reshetikhin. Our formulas and method of proof even in the symmetric and anti-symmetric cases are different from the work of Hatayama et~al. We interpret the fermionic formulas in terms of a new set of unrestricted rigged configurations. For the proof we give a statistics preserving bijection from this new set of unrestricted rigged configurations to the set of unrestricted crystal paths which generalizes a bijection of Kirillov and Reshetikhin. We also present new fermionic formulas for the characters of N=1 and N=2 superconformal algebras which extend the work of Berkovich, McCoy and Schilling. We present fermionic formulas for the...
