DOAJ Open Access 2014

Schubert varieties, inversion arrangements, and Peterson translation

William Slofstra

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Abstrak

We show that an element $\mathcal{w}$ of a finite Weyl group W is rationally smooth if and only if the hyperplane arrangement $\mathcal{I} (\mathcal{w})$ associated to the inversion set of \mathcal{w} is inductively free, and the product $(d_1+1) ...(d_l+1)$ of the coexponents $d_1,\ldots,d_l$ is equal to the size of the Bruhat interval [e,w]. We also use Peterson translation of coconvex sets to give a Shapiro-Steinberg-Kostant rule for the exponents of $\mathcal{w}$.

Topik & Kata Kunci

Mathematics

Penulis (1)

William Slofstra

Format Sitasi

APA MLA BibTeX

Slofstra, W. (2014). Schubert varieties, inversion arrangements, and Peterson translation. https://doi.org/10.46298/dmtcs.2436

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2436

Informasi Jurnal

Tahun Terbit: 2014
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2436
Akses: Open Access ✓