Global representations of the Heat and Schrödinger equation with singular potential

2011/10/05 by Jose Franco, Franco, Jose, Mark Sepanski +1
Mathematics · #22E70 #35Q41 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:22E70 #msc:35Q41

paper · pdf · doi:10.48550/arxiv.1110.1030

arxiv created 2013/02/15 · arxiv updated 2013/02/18

Abstract

We study the n-dimensional Schrödinger equation with singular potential V_λ(x)=λ|x|^-2. Its solution space is studied as a global representation of \widetildeSL(2,\R)× O(n). A special subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. The space of K-finite vectors is calculated, obtaining conditions for λ so that this space is non-empty. The direct sum of solution spaces, over such admissible values of λ is studied as a representation of the 2n+1-dimensional Heisenberg group.

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