Illinois Journal of Mathematics

Invariant CR mappings between hyperquadrics

Dusty Grundmeier, Kemen Linsuain, and Brendan Whitaker

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Abstract

We analyze a canonical construction of group-invariant CR Mappings between hyperquadrics due to D’Angelo. Given source hyperquadric of $Q(1,1)$, we determine the signature of the target hyperquadric for all finite subgroups of $SU(1,1)$. We also extend combinatorial results proven by Loehr, Warrington, and Wilf on determinants of sparse circulant determinants. We apply these results to study CR mappings invariant under finite subgroups of $U(1,1)$.

Article information

Source
Illinois J. Math., Volume 62, Number 1-4 (2018), 321-340.

Dates
Received: 15 March 2018
Revised: 31 July 2018
First available in Project Euclid: 13 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1552442665

Digital Object Identifier
doi:10.1215/ijm/1552442665

Mathematical Reviews number (MathSciNet)
MR3922419

Zentralblatt MATH identifier
07036789

Subjects
Primary: 32V20: Analysis on CR manifolds 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14] 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 32H35: Proper mappings, finiteness theorems

Citation

Grundmeier, Dusty; Linsuain, Kemen; Whitaker, Brendan. Invariant CR mappings between hyperquadrics. Illinois J. Math. 62 (2018), no. 1-4, 321--340. doi:10.1215/ijm/1552442665. https://projecteuclid.org/euclid.ijm/1552442665


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