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- W2949558511 abstract "We construct a unique G-equivariant graded star product on the algebra $S(g)/I$ of polynomial functions on the minimal nilpotent coadjoint orbit $Omin$ of G where G is a complex simple Lie group and $gneqsl_2(C)$. This strengthens the result of Arnal, Benamor, and Cahen. Our main result is to compute, for G classical, the star product of a momentum function $mu_x$ with any function f. We find $mu_xstar f=mu_xf+half{mu_x,f}t+Lambda^x(f)t^2$. For $g$ different from $sp_n(C)$, $Lambda^x$ is not a differential operator. Instead $Lamda^x$ is the left quotient of an explicit order 4 algebraic differential operator $D^x$ by an order 2 invertible diagonalizable operator. Precisely, $Lambda^x=-{1/4}frac{1}{E'(E'+1)}D^x$ where $E'$ is a positive shift of the Euler vector field. Thus $mu_xstar f$ is not local in f. Using $star$ we construct a positive definite hermitian inner product on $Sg/I$. The Hilbert space completion of $Sg/I$ is then a unitary representation of $G$. This quantizes $Omin$ in the sense of geometric quantization and the orbit method." @default.
- W2949558511 created "2019-06-27" @default.
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- W2949558511 date "2000-10-27" @default.
- W2949558511 modified "2023-09-27" @default.
- W2949558511 title "Non-Local Equivariant Star Product on the Minimal Nilpotent Orbit" @default.
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