Relation between two geometrically defined bases in representations of $GL_n$
| dc.creator | Braverman, Alexander | |
| dc.creator | Gaitsgory, Dennis | |
| dc.creator | Vybornov, Maxim | |
| dc.date | 2004-11-11 | |
| dc.date | 2006-07-11 | |
| dc.date.accessioned | 2026-07-07T06:38:59Z | |
| dc.date.available | 2026-07-07T06:38:59Z | |
| dc.description | Let $V$ be an irreducible representation of group $GL_n({\mathbb C})$, which appears as a submodule in $({\mathbb C}^n)^{\otimes d}$, where ${\mathbb C}^n$ is the tautological $n$-dimensional representation of $GL_n$, and $d$ is a non-negative integer. On the one hand, following refs [Gi] and [BG] one can produce a basis in $V$ using irreducible components of Sringer fibers over a nilpotent matrix in ${\mathfrak {gl}}_d$, whose Jordan blocks correspond to the highest weight of $V$. On the other hand, one can produce a basis in $V$ by Mirković-Vilonen cycles, a construction that works for an arbitrary reductive group $G$. In this note we prove that the resulting to bases coincide. | |
| dc.identifier | https://arxiv.org/abs/math/0411252 | |
| dc.identifier | http://arxiv.org/abs/math/0411252 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100935 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Relation between two geometrically defined bases in representations of $GL_n$ | |
| dc.type | text |