标题： 二维二阶量子超可积系统的收缩理论及其与超几何正交多项式阿斯凯方案的关系 显示英文标题

标题： The theory of contractions of 2D 2nd order quantum superintegrable systems and its relation to the Askey scheme for hypergeometric orthogonal polynomials

摘要： 我们描述了二阶超可积系统的收缩理论，表明二维的所有此类系统都是单个系统的极限情况：我们在列表中的2-球面上的通用3参数势，即S9。 类似地，这些系统的二次对称性代数都可以通过从S9开始的一系列收缩得到。 通过将S9代数不可约表示的函数空间实现（给出Racah/Wilson多项式的结构方程）收缩到其他超可积系统，可以得到正交超几何多项式的完整Askey方案。这直接将该方案与显式可解的量子力学系统联系起来。 令人惊讶的是，所有具有势的超可积系统的收缩都是由so(3,C)和e(2,C)的Wigner李代数收缩唯一诱导的。 本文重点描述李代数和超可积系统收缩之间的这种密切联系，详细计算则在其他地方展示。 与E. Kalnins、S. Post、E. Subag和R. Heinonen的合作成果 显示英文摘要

摘要： We describe a contraction theory for 2nd order superintegrable systems, showing that all such systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. Analogously, all of the quadratic symmetry algebras of these systems can be obtained by a sequence of contractions starting from S9. By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials.This relates the scheme directly to explicitly solvable quantum mechanical systems. Amazingly, all of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3,C) and e(2,C). The present paper concentrates on describing this intimate link between Lie algebra and superintegrable system contractions, with the detailed calculations presented elsewhere. Joint work with E. Kalnins, S. Post, E. Subag and R. Heinonen