DOAJ Open Access 2009

A preorder-free construction of the Kazhdan-Lusztig representations of $S_n$, with connections to the Clausen representations

Charles Buehrle Mark Skandera

Lihat Sumber DOI

Abstrak

We use the polynomial ring $\mathbb{C}[x_{1,1},\ldots,x_{n,n}]$ to modify the Kazhdan-Lusztig construction of irreducible $S_n$-modules. This modified construction produces exactly the same matrices as the original construction in [$\textit{Invent. Math}$ $\mathbf{53}$ (1979)], but does not employ the Kazhdan-Lusztig preorders. We also show that our modules are related by unitriangular transition matrices to those constructed by Clausen in [$\textit{J. Symbolic Comput.}$ $\textbf{11}$ (1991)]. This provides a $\mathbb{C}[x_{1,1},\ldots,x_{n,n}]$-analog of results of Garsia-McLarnan in [$\textit{Adv. Math.}$ $\textbf{69}$ (1988)].

Topik & Kata Kunci

Mathematics

Penulis (2)

Charles Buehrle

Mark Skandera

Format Sitasi

APA MLA BibTeX

Buehrle, C., Skandera, M. (2009). A preorder-free construction of the Kazhdan-Lusztig representations of $S_n$, with connections to the Clausen representations. https://doi.org/10.46298/dmtcs.2736

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2736

Informasi Jurnal

Tahun Terbit: 2009
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2736
Akses: Open Access ✓