2026-09-21T00:40:11Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/24090 2023-07-10 col_2142_16340 col_2142_5131 com_2142_16339 com_2142_8903 com_2142_5130

D'Angelo, John P. Tyson, Jeremy T. D'Angelo, John P. Leininger, Christopher J. Lebl, Jiri Grundmeier, Dusty E. 2011-05-25T15:05:03Z 2011-05-25T15:05:03Z 2011-05-25T15:05:03Z 2011-05 We consider group-invariant CR mappings from spheres to hyperquadrics. Given a finite subgroup $\Gamma \subset U(n)$, a construction of D'Angelo and Lichtblau yields a target hyperquadric $Q(\Gamma)$ and a canonical non-constant CR map $h_{\Gamma} : S^{2n-1}/\Gamma \to Q(\Gamma)$. For every $\Gamma \subset SU(2)$, we determine this hyperquadric $Q(\Gamma)$, that is, the numbers of positive and negative eigenvalues in its defining equation. For families of cyclic and dihedral subgroups of $U(2)$, we study these numbers asymptotically as the order of the group tends to infinity. Next we study number-theoretic and combinatorial aspects of $h_{\Gamma}$ for cyclic $\Gamma \subset U(2)$. In particular, we show that the mappings $h_{\Gamma}$ associated to the lens spaces $L(p,q)$ satisfy a linear recurrence relation of order $2^q-1$ and no smaller. We also give explicit but complicated formulas for the coefficients. Finally, we explore connections with representation theory and invariant theory. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-04-12T21:03:19Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 4 sourcecode.tex: 1236 bytes, checksum: 00af13ea4f8f71a4b923751e87006cbd (MD5) thesisrefs.bib: 5413 bytes, checksum: ca7da7aa0bf510f1e2b9fc4fe5838572 (MD5) grundmeierthesis.tex: 146006 bytes, checksum: 8308d934a3623a103d06f35b530a617b (MD5) Grundmeier_Dusty.pdf: 642581 bytes, checksum: bad7c48d0d176247b47c2368e05775d6 (MD5) Made available in DSpace on 2011-05-25T15:05:03Z (GMT). No. of bitstreams: 5 Grundmeier_Dusty.pdf: 643019 bytes, checksum: 89b815d29d7ed8a94cea9f327fef8c99 (MD5) license.txt: 4066 bytes, checksum: 8ff40cab9dad748cb2b4bf5791545660 (MD5) thesisrefs.bib: 5413 bytes, checksum: ca7da7aa0bf510f1e2b9fc4fe5838572 (MD5) sourcecode.tex: 1236 bytes, checksum: 00af13ea4f8f71a4b923751e87006cbd (MD5) grundmeierthesis.tex: 146049 bytes, checksum: 5c28c1b025daa52770d194a91989eabb (MD5) http://hdl.handle.net/2142/24090 en Copyright 2011 Dusty E. Grundmeier Group-Invariant CR Mappings Hermitian Polynomials mappings to hyperquadrics Group-invariant CR mappings Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD