无限制Kostka多项式的费米公式与超共形特征标
Fermionic Formulas For Unrestricted Kostka Polynomials And Superconformal Characters
摘要：
Kostka多项式的推广和共形域论的特征的费米子公式的寻找是近几十年来一个非常令人兴奋的研究课题。在这篇论文中，我们提出了新的费米子公式的无限制Kostka多项式扩展的工作Kirillov和Reshetikhin。我们还给出了N=1和N=2超共形代数特征标的新的费米子公式，推广了Berkovich，McCoy和Schilling的工作. Hatayama等人给出了$A_{n-1}^{(1)}$型非限制Kostka多项式在对称和反对称晶路情况下的费米子公式，我们基于Kirillov-Reshetihkin模给出了$A_{n-1}^{(1)}$型非限制Kostka多项式在所有晶路情况下的新的费米子公式.我们解释的费米子公式的一组新的无限制的操纵配置。利用Bailey引理，通过建立从非酉极小模型到超共形模型的新Bailey流，导出了N=1和N=2超共形代数的费米子公式.
英文摘要：
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 dissertation we present new fermionic formulas for the unrestricted Kostka polynomials extending the work 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. Fermionic formulas for the unrestricted Kostka polynomials of type $A_{n-1}^{(1)}$ in the case of symmetric and anti-symmetric crystal paths were given by Hatayama et al. We present new fermionic formulas for the unrestricted Kostka polynomials of type $A_{n-1}^{(1)}$ for all crystal paths based on Kirillov-Reshetihkin modules. We interpret the fermionic formulas in terms of a new set of unrestricted rigged configurations. Fermionic formulas for the N=1 and N=2 superconformal algebras are derived using the Bailey lemma by establishing new Bailey flows from the nonunitary minimal models to the superconformal models.
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