Kraft, Hanspeter and Wallach, Nolan. (2010) Polarizations and Nullcone of Representations of Reductive Groups. Progress in mathematics, Vol. 278. pp. 153168.

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Abstract
The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the nqubits which appear in quantum computing. This is the representation of a product of n copies of $SL_2$ on the nfold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119140.)
Faculties and Departments:  05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft) 

UniBasel Contributors:  Kraft, Hanspeter 
Item Type:  Article, refereed 
Article Subtype:  Research Article 
Note:  Also published in: Symmetry and spaces.  Boston : BirkhĂ¤user, 2010.  S. 153168  Publication type according to Uni Basel Research Database: Journal article 
Language:  English 
Last Modified:  21 Jun 2018 14:22 
Deposited On:  22 Mar 2012 13:59 
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