Spherical varieties
http://relaunch.hcm.uni-bonn.de/fileadmin/perrin/spherical.pdf Web1. júl 2008 · We generalize this description to an arbitrary spherical variety X of G as follows. Irreducible unramified quotients of the space are in natural ‘almost bijection’ with a number of copies of A X * / W X, the quotient of a complex torus by the ‘little Weyl group’ of X. This leads to a description of the Hecke module of unramified vectors ...
Spherical varieties
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WebIn short, the visibility is a geometric condition that assures the multiplicity-freeness property. In this article we consider the converse direction when U U is a compact real form of a connected complex reductive algebraic group G G and X X is an irreducible complex algebraic G G -variety. In this setting the multiplicity-freeness property of ... Web29. apr 2024 · M. Huruguen, Toric varieties and spherical embeddings over an arbitrary field, J. Algebra 342 (2011), 212–234. Article MathSciNet Google Scholar J. Jahnel, The …
WebSpherical varieties A complex algebraic variety is a spherical variety if it’s acted upon by a reductive group G and there is a dense orbit under the action of a Borel subgroup B. Reductive groups include semisimple groups (e.g., SL n, symplectic groups, orthogonal groups), tori (C)n, and general linear groups. Web5. máj 2024 · For arbitrary spherical varieties the answer is no in general. If my memory serves me right, the spherical variety $Sp (4,\mathbb C)/ (\mathbb C^*\times SL (2,\mathbb C))$ is a counterexample. As far as I know, the $H$ -orbit structure of $G/H$ is still unknown in full generality.
Web10. júl 2024 · Spherical varieties (spherical homogeneous spaces and spherical embeddings) were considered in works of Luna, Vust, Brion, Knop, Losev, and others. The classification of spherical homogeneous spaces over algebraically closed fields of characteristic $0$ was completed in the works of Losev [ 37 ] and Bravi and Pezzini [ 13 … WebIf the address matches an existing account you will receive an email with instructions to reset your password
Webgeneral spherical varieties. Remark 1.1. The de nitions of m geom(ˇ;˜) and I geom(f) are very similar to each other. So one only needs to de ne m geom(ˇ;˜) for general spherical varieties, which will lead to the de nition of I geom(f). In this paper, we propose a uniform de nition of m geom(ˇ;˜) (and hence I geom(f)) for general spherical ...
WebA normal G-variety X is called spherical if a Borel subgroup of G has a dense orbit in X. Of particular interest are spherical varieties which are smooth and affine since they form … merhoff and larkinWebTY - JOUR AU - Bravi, Paolo TI - Classification of spherical varieties JO - Les cours du CIRM PY - 2010 PB - CIRM VL - 1 IS - 1 SP - 99 EP - 111 AB - We give a short introduction to the problem of classification of spherical varieties, by presenting the Luna conjecture about the classification of wonderful varieties and illustrating some of the ... how old to join crunch fitnessWeb1. Spherical varieties 1.1. What is a spherical variety? A G-variety Xover F qis called spherical if X kis a normal variety with an open dense orbit of a Borel B kˆG k after base change to k. One should think of this as a niteness property. For example, Brion proved the above de nition is equivalent to X k having nitely many B k orbits. The ... how old to horses live