Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials

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• 作者：Francesco Brenti^a ; ^{brenti@mat.uniroma2.it" class="auth_mail" title="E-mail the corresponding author} ; Fabrizio Caselli^b ; ^{fabrizio.caselli@unibo.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05E10
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：2 January 2017
• 年：2017
• 卷：304
• 期：Complete
• 页码：539-582
• 全文大小：738 K

文摘

We give a new characterization of the peak subalgebra of the algebra of quasisymmetric functions and use this to construct a new basis for this subalgebra. As an application of these results we obtain a combinatorial formula for the Kazhdan–Lusztig polynomials which holds in complete generality and is simpler and more explicit than any existing one. We point out that, in a certain sense, this formula cannot be simplified.