Defining equations for supergroup orbits in super Clifford modules. (English) Zbl 0719.22005
It is known that, if \(\{\Lambda^ k(C^ n)\}\) are fundamental representations of gl(n,C) over the Clifford algebra of the fermionic creation and annihilation operators \(\{\psi_ i,\psi_ i^*\}\), the \(v\in \Lambda^ k(C^ n)\) satisfying the Plücker equation \(\sum^{n}_{i=1}\psi_ iv\otimes \psi_ i^*v=0\) form the Gl(n,C) orbit of the highest weight vector of \(\Lambda^ k(C^ n).\)
The paper generalises this result. A super Clifford module defines representations \(M_{k,m}\) of the super Lie algebra \(gl_{p| q}\). A generalised Plücker equation describes a group orbit of the maximal subgroup of the supergroup \(GL_{p| q}\), acting on representations \(M_{k,m}\).
The paper generalises this result. A super Clifford module defines representations \(M_{k,m}\) of the super Lie algebra \(gl_{p| q}\). A generalised Plücker equation describes a group orbit of the maximal subgroup of the supergroup \(GL_{p| q}\), acting on representations \(M_{k,m}\).
Reviewer: J.S.R.Chisholm (Canterbury)
MSC:
22E65 | Infinite-dimensional Lie groups and their Lie algebras: general properties |
17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
17B65 | Infinite-dimensional Lie (super)algebras |
17A70 | Superalgebras |
22E70 | Applications of Lie groups to the sciences; explicit representations |
58C50 | Analysis on supermanifolds or graded manifolds |
Keywords:
fundamental representations; Clifford algebra; fermionic creation and annihilation operators; Plücker equation; super Clifford module; super Lie algebra; group orbit; supergroupReferences:
[1] | DOI: 10.1073/pnas.80.6.1778 · Zbl 0512.17008 · doi:10.1073/pnas.80.6.1778 |
[2] | DOI: 10.5802/aif.1113 · Zbl 0625.58041 · doi:10.5802/aif.1113 |
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