Mathematics - Ph.D. / Sc.D.
http://hdl.handle.net/1721.1/7680
2015-04-29T03:04:35ZAn Erlanger program for combinatorial geometries.
http://hdl.handle.net/1721.1/95532
An Erlanger program for combinatorial geometries.
Kung, Joseph Pee Sin
Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.; Vita.; Bibliography: leaves 132-137.
1978-01-01T00:00:00ZOn moduli stacks of finite group schemes
http://hdl.handle.net/1721.1/93003
On moduli stacks of finite group schemes
Zhang, Zhaohui, 1972-
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2000.; Includes bibliographical references (p. 41-42).
2000-01-01T00:00:00ZWitt spaces : a geometric cycle theory for KO-homology at odd primes.
http://hdl.handle.net/1721.1/91309
Witt spaces : a geometric cycle theory for KO-homology at odd primes.
Siegel, Paul Howard
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.; Vita.; Bibliography: leaves 131-133.
1979-01-01T00:00:00ZThe affine Yangian of gl₁, and the infinitesimal Cherednik algebras
http://hdl.handle.net/1721.1/90192
The affine Yangian of gl₁, and the infinitesimal Cherednik algebras
Tsymbaliuk, Oleksandr
In the first part of this thesis, we obtain some new results about infinitesimal Cherednik algebras. They have been introduced by Etingof-Gan-Ginzburg in [EGG] as appropriate analogues of the classical Cherednik algebras, corresponding to the reductive groups, rather than the finite ones. Our main result is the realization of those algebras as particular finite W-algebras of associated semisimple Lie algebras with nilpotent 1-block elements. To achieve this, we prove its Poisson counterpart first, which identifies the Poisson infinitesimal Cherednik algebras introduced in [DT] with the Poisson algebras of regular functions on the corresponding Slodowy slices. As a consequence, we obtain some new results about those algebras. We also generalize the classification results of [EGG] from the cases GL, and SP2n to SOl. In the second part of the thesis, we discuss the loop realization of the affine Yangian of gl₁. Similar objects were recently considered in the work of Maulik-Okounkov on the quantum cohomology theory, see [MO]. We present a purely algebraic realization of these algebras by generators and relations. We discuss some families of their representations. A similarity with the representation theory of the quantum toroidal algebra of gl₁ is explained by adapting a recent result of Gautam-Toledano Laredo, see [GTL], to the local setting. We also discuss some aspects of those two algebras such as the degeneration isomorphism, a shuffle presentation, and a geometric construction of the Whittaker vectors.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 183-186).
2014-01-01T00:00:00Z