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Monogenic functions and representations of nilpotent Lie groups in quantum mechanics
Author(s) -
Cnops Jan,
Kisil Vladimir V.
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19990310)22:4<353::aid-mma44>3.0.co;2-#
Subject(s) - mathematics , holomorphic function , nilpotent , lie group , pure mathematics , heisenberg group , lie algebra , representation theory , algebra over a field , adjoint representation , nilpotent group , representation of a lie group , fundamental representation , representation (politics) , simple lie group , space (punctuation) , linguistics , philosophy , politics , political science , law , weight
We describe several different representations of nilpotent step two Lie groups in spaces of monogenic Clifford‐valued functions. We are inspired by the classic representation of the Heisenberg group in the Segal–Bargmann space of holomorphic functions. Connections with quantum mechanics are described. Copyright © 1999 John Wiley & Sons, Ltd.