Exotic Differential Operators on Complex Minimal Nilpotent Orbits
| dc.creator | Astashkevich, A. | |
| dc.creator | Brylinski, R. | |
| dc.date | 1997-11-26 | |
| dc.date | 1998-06-30 | |
| dc.date.accessioned | 2026-07-07T06:32:38Z | |
| dc.date.available | 2026-07-07T06:32:38Z | |
| dc.description | Let O be the minimal nilpotent adjoint orbit in a classical complex semisimple Lie algebra g. O is a smooth quasi-affine variety stable under the Euler dilation action $C^*$ on g. The algebra of differential operators on O is D(O)=D(Cl(O)) where the closure Cl(O) is a singular cone in g. See \cite{jos} and \cite{bkHam} for some results on the geometry and quantization of O. We construct an explicit subspace $A_{-1}\subset D(O)$ of commuting differential operators which are Euler homogeneous of degree -1. The space $A_{-1}$ is finite-dimensional, g-stable and carries the adjoint representation. $A_{-1}$ consists of (for $g \neq sp(2n,C)$) non-obvious order 4 differential operators obtained by quantizing symbols we obtained previously. These operators are "exotic" in that there is (apparently) no geometric or algebraic theory which explains them. The algebra generated by $A_{-1}$ is a maximal commutative subalgebra A of D(X). We find a G-equivariant algebra isomorphism R(O) to A, $f\mapsto D_f$, such that the formula $(f|g)=({constant term of}D_{\bar{g}} f)$ defines a positive-definite Hermitian inner product on R(O). We will use these operators $D_f$ to quantize O in a subsequent paper. | |
| dc.description | 34 pages, corrected some typos, changed content | |
| dc.identifier | https://arxiv.org/abs/q-alg/9711023 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9711023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98959 | |
| dc.subject | Quantum Algebra | |
| dc.title | Exotic Differential Operators on Complex Minimal Nilpotent Orbits | |
| dc.type | text |