Locally convex curves and the Bruhat stratification of the spin group
| Autor: | Goulart, Victor, Saldanha, Nicolau C. |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11856-021-2127-z |
| Popis: | We study the lifting of the Schubert stratification of the homogeneous space of complete real flags of $R^{n+1}$ to its universal covering group $Spin_{n+1}$. We call the lifted strata the Bruhat cells of $Spin_{n+1}$, in keeping with the homonymous classical decomposition of reductive algebraic groups. We present explicit parameterizations for these Bruhat cells in terms of minimal-length expressions $\sigma=a_{i_1}... a_{i_k}$ for permutations $\sigma\in S_{n+1}$ in terms of the $n$ generators $a_i=(i,i+1)$. These parameterizations are compatible with the Bruhat orders in the Coxeter-Weyl group $S_{n+1}$. This stratification is an important tool in the study of locally convex curves; we present a few such applications. Comment: 34 pages, 1 figure, minor revisions. There is a strong overlap in content with arXiv:1810.08632 |
| Databáze: | arXiv |
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