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oai:www.ideals.illinois.edu:2142/87004 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Maarten Bergvelt Kilmurray, Donough 2015-09-28T15:20:34Z 2015-09-28T15:20:34Z 10000-01-01 2000 2000 We introduce a new factorization for elements of the loop group LSL2 = SL2( C ((lambda-1))). We then define a new decomposition for the flag manifold FL2 = LSL2/ B+ (= SL2&d14;/B&d14; + ), into isomorphic overlapping cells. This allows us to examine globally the left vector field action of the homogeneous Heisenberg subalgebra Hsl2 on FL2. On each cell of the quotient H -\FL2, we find coordinates for the modified non-linear Schrodinger (mNLS) hierarchy, with Miura, maps to NLS coordinates on the Grassmannian. We also find transformation rules relating coordinates across cells. The right vector field action of n&d14;-⊂ sl2&d14; attaches to the coordinate ring of each cell an object e +/-2&phis;. We show that this gives a special line bundle structure on H-\FL2. Finally, we define on each cell a Hamiltonian structure. This leads to a vertex algebra structure, and from the n&d14;- -action, a vertex algebra module structure, on each cell. We establish the compatibility of these structures across cells to show that H -\FL2 is a vertex variety, i.e. a variety whose structure sheaf is a sheaf of vertex algebras. Made available in DSpace on 2015-09-28T15:20:34Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9990040.pdf: 3832310 bytes, checksum: 422131aa01cd59c204594198fb57281f (MD5) Previous issue date: 2000 Embargo set by: Seth Robbins for item 88285 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 85 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000. http://hdl.handle.net/2142/87004 (MiAaPQ)AAI9990040 eng Mathematics Geometry of Affine Actions text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.