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On the nullcone of
representations of reductive groups
Hanspeter Kraft and Nolan R. Wallach |
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Vol. 224 (2006), No. 1, 119–139
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Abstract |
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We study the geometry of the nullcone N = NV ⊕k for several copies of a representation V of a reductive group G and its behavior for different k. We show that for large k there is a certain “stability” with respect to the irreducible components. In the case of the so-called 𝜃-representations, this can be made more precise by using the combinatorics of the weight system as a subset of the root system. All this finally allows us to calculate explicitly and in detail a number of important examples, such as the cases of 3- and 4-qubits, which play a fundamental rôle in quantum computing. |
Keywords
nullcone, invariant, qubit, 𝜃-representation
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Mathematical Subject Classification 2000
Primary: 20G20, 20G05, 14L24
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Milestones
Received: 21 February 2005
Accepted: 25 September 2005
Published: 1 March 2006
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Authors |
| Hanspeter Kraft | |
| Mathematisches Institut der
Universität Basel Rheinsprung 21 CH-4051 Basel Switzerland |
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| Nolan R. Wallach | |
| Department of Mathematics University of California, San Diego 9500 Gilman Drive La Jolla, CA 92093-0112 United States |
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