Simply-laced Coxeter groups and groups generated by symplectic transvections
| dc.creator | Shapiro, Boris | |
| dc.creator | Shapiro, Michael | |
| dc.creator | Vainshtein, Alek | |
| dc.creator | Zelevinsky, Andrei | |
| dc.date | 1999-06-29 | |
| dc.date.accessioned | 2026-07-07T05:29:42Z | |
| dc.date.available | 2026-07-07T05:29:42Z | |
| dc.description | Let W be an arbitrary Coxeter group of simply-laced type (possibly infinite but of finite rank), u,v be any two elements in W, and i be a reduced word (of length m) for the pair (u,v) in the Coxeter group W\times W. We associate to i a subgroup Gamma_i in GL_m(Z) generated by symplectic transvections. We prove among other things that the subgroups corresponding to different reduced words for the same pair (u,v) are conjugate to each other inside GL_m(Z). We also generalize the enumeration result of the first three authors (see AG/9802093) by showing that, under certain assumptions on u and v, the number of Gamma_i(F_2)-orbits in F_2^m is equal to 3\times 2^s, where s is the number of simple reflections that appear in a reduced decomposition for u or v and F_2 is the two-element field. | |
| dc.description | LaTeX, 18 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/9906203 | |
| dc.identifier | http://arxiv.org/abs/math/9906203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78744 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | Primary 20F55; Secondary 05E15, 14N10 | |
| dc.title | Simply-laced Coxeter groups and groups generated by symplectic transvections | |
| dc.type | text |