dorsal/arxiv
View SchemaA Star Product for Complex Grasmann Manifolds
| Authors | Joachim Schirmer |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9709021 |
| URL | https://arxiv.org/abs/q-alg/9709021 |
Abstract
We explicitly construct a star product for the complex Grassmann manifolds using the method of phase space reduction. Functions on $\mathbb{C}^{(p+q)\cdot p~*}$, the space of $(p+q)\times p$ matrices of rank p, invariant under the right action of $Gl(p,\mathbb{C})$ can be regarded as functions on the Grassmann manifold $G_{p,q}(\mathbb{C})$, but do not form a subalgebra whereas functions only invariant under the unitary subgroup $U(p)\subset Gl(p,\mathbb{C})$ do. The idea is to construct a projection from $U(p)$- onto $Gl(p,\mathbb{C})$-invariant functions, whose kernel is an ideal. This projection can be used to define a star-algebra on $G_{p,q}(\mathbb{C})$ onto which this projection acts as an algebra-epimorphism.
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"date_modified": "2026-03-02T18:01:28.823000Z",
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"abstract": "We explicitly construct a star product for the complex Grassmann manifolds\nusing the method of phase space reduction. Functions on $\\mathbb{C}^{(p+q)\\cdot\np~*}$, the space of $(p+q)\\times p$ matrices of rank p, invariant under the\nright action of $Gl(p,\\mathbb{C})$ can be regarded as functions on the\nGrassmann manifold $G_{p,q}(\\mathbb{C})$, but do not form a subalgebra whereas\nfunctions only invariant under the unitary subgroup $U(p)\\subset\nGl(p,\\mathbb{C})$ do. The idea is to construct a projection from $U(p)$- onto\n$Gl(p,\\mathbb{C})$-invariant functions, whose kernel is an ideal. This\nprojection can be used to define a star-algebra on $G_{p,q}(\\mathbb{C})$ onto\nwhich this projection acts as an algebra-epimorphism.",
"arxiv_id": "q-alg/9709021",
"authors": [
"Joachim Schirmer"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "A Star Product for Complex Grasmann Manifolds",
"url": "https://arxiv.org/abs/q-alg/9709021"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "705df063-9203-4513-8549-10c3fd012239",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
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