Geodesic
GOLDIE RANK OF PRIMITIVE QUOTIENTS VIA LATTICE POINT ENUMERATION
Glasgow mathematical journal, Tome 55 (2013) no. A, pp. 149-168

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DOI

Let k be an algebraically closed field of characteristic zero. I. M. Musson and M. Van den Bergh (Mem. Amer. Math. Soc., vol. 136, 1998, p. 650) classify primitive ideals for rings of torus invariant differential operators. This classification applies in particular to subquotients of localized extended Weyl algebras $\mathcal{A}_{r,n-r}=k[x_1,\ldots,x_r,x_{r+1}^{\pm1}, \ldots, x_{n}^{\pm1},\partial_1,\ldots,\partial_n],$ where it can be made explicit in terms of convex geometry. We recall these results and then turn to the corresponding primitive quotients and study their Goldie ranks. We prove that the primitive quotients fall into finitely many families whose Goldie ranks are given by a common quasi-polynomial and then realize these quasi-polynomials as Ehrhart quasi-polynomials arising from convex geometry.
DOI : 10.1017/S0017089513000566
Mots-clés : 17B10, 16S32, 52B20 
MEINEL, JOANNA; STROPPEL, CATHARINA. GOLDIE RANK OF PRIMITIVE QUOTIENTS VIA LATTICE POINT ENUMERATION. Glasgow mathematical journal, Tome 55 (2013) no. A, pp. 149-168. doi: 10.1017/S0017089513000566
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     title = {GOLDIE {RANK} {OF} {PRIMITIVE} {QUOTIENTS} {VIA} {LATTICE} {POINT} {ENUMERATION}},
     journal = {Glasgow mathematical journal},
     pages = {149--168},
     year = {2013},
     volume = {55},
     number = {A},
     doi = {10.1017/S0017089513000566},
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