TY - JOUR
T1 - On the space of $ K$-finite solutions to intertwining differential operators
AU - Kubo, Toshihisa
AU - Orsted, Bent
PY - 2019/9
Y1 - 2019/9
N2 - In this paper we give Peter-Weyl-type decomposition theorems for the space of K-finite solutions to intertwining differential operators between parabolically induced representations. Our results generalize a result of Kable for conformally invariant systems. The main idea is based on the duality theorem between intertwining differential operators and homomorphisms between generalized Verma modules. As an application we uniformly realize on the solution spaces of intertwining differential operators all small representations of SL(3,ℝ) attached to the minimal nilpotent orbit.
AB - In this paper we give Peter-Weyl-type decomposition theorems for the space of K-finite solutions to intertwining differential operators between parabolically induced representations. Our results generalize a result of Kable for conformally invariant systems. The main idea is based on the duality theorem between intertwining differential operators and homomorphisms between generalized Verma modules. As an application we uniformly realize on the solution spaces of intertwining differential operators all small representations of SL(3,ℝ) attached to the minimal nilpotent orbit.
KW - CONFORMALLY INVARIANT-SYSTEMS
KW - HEISENBERG ULTRAHYPERBOLIC EQUATION
KW - Intertwining differential operators
KW - K-finite solutions
KW - MINIMAL REPRESENTATION
KW - O(P
KW - Peter-Weyl-type formulas
KW - SINGULAR REPRESENTATION
KW - SL(3
KW - Torasso's representation
KW - UNITARY REPRESENTATIONS
KW - duality theorem
KW - generalized Verma modules
KW - hypergeometric polynomials
KW - small representations
UR - http://www.scopus.com/inward/record.url?scp=85073965519&partnerID=8YFLogxK
U2 - 10.1090/ert/527
DO - 10.1090/ert/527
M3 - Journal article
SN - 1088-4165
VL - 23
SP - 213
EP - 248
JO - Representation Theory
JF - Representation Theory
IS - 7
ER -