Bethe algebra and algebra of functions on the space of differential operators of order two with polynomial solutions

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dc.creatorMukhin, E.
dc.creatorTarasov, V.
dc.creatorVarchenko, A.
dc.date2007-05-28
dc.date.accessioned2026-07-07T08:03:26Z
dc.date.available2026-07-07T08:03:26Z
dc.descriptionWe show that the following two algebras are isomorphic. The first is the algebra $A_P$ of functions on the scheme of monic linear second-order differential operators on $\C$ with prescribed regular singular points at $z_1,..., z_n, \infty$, prescribed exponents $\La^{(1)}, ..., \La^{(n)}, \La^{(\infty)}$ at the singular points, and having the kernel consisting of polynomials only. The second is the Bethe algebra of commuting linear operators, acting on the vector space $\Sing L_{\La^{(1)}} \otimes ... \otimes L_{\La^{(n)}}[\La^{(\infty)}]$ of singular vectors of weight $\La^{(\infty)}$ in the tensor product of finite dimensional polynomial $gl_2$-modules with highest weights $\La^{(1)},..., \La^{(n)}$.
dc.identifierhttps://arxiv.org/abs/0705.4114
dc.identifierhttp://arxiv.org/abs/0705.4114
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129581
dc.subjectQuantum Algebra
dc.subjectAlgebraic Geometry
dc.subjectClassical Analysis and ODEs
dc.titleBethe algebra and algebra of functions on the space of differential operators of order two with polynomial solutions
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