112 research outputs found
Developments and retrospectives in Lie theory: algebraic methods
No full textThis volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics. Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Algebraic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current research. Most of the workshops have taken place at leading public and private universities in California, though on occasion workshops have taken place in Oregon, Louisiana and Utah. Experts in representation theory/Lie theory from various parts of the Americas, Europe and Asia have given talks at these meetings. The workshop series is robust, and the meetings continue on a quarterly basis. Contributors to the Algebraic Methods volume: Y. Bahturin, C. P. Bendel, B.D. Boe, J. Brundan, A. Chirvasitu, B. Cox, V. Dolgushev, C.M. Drupieski, M.G. Eastwood, V. Futorny, D. Grantcharov, A. van Groningen, M. Goze, J.-S. Huang, A.V. Isaev, I. Kashuba, R.A. Martins, G. Mason, D. Miličić, D.K., Nakano, S.-H. Ng, B.J. Parshall, I. Penkov, C. Pillen, E. Remm, V. Serganova, M.P. Tuite, H.D. Van, J.F. Willenbring, T. Willwacher, C.B. Wright, G. Yamskulna, G. Zuckerma
Cartan subalgebras of root-reductive Lie algebras
No full textAbstractRoot-reductive Lie algebras are direct limits of finite-dimensional reductive Lie algebras under injections which preserve the root spaces. It is known that a root-reductive Lie algebra is a split extension of an abelian Lie algebra by a direct sum of copies of finite-dimensional simple Lie algebras as well as copies of the three simple infinite-dimensional root-reductive Lie algebras sl∞, so∞, and sp∞. As part of a structure theory program for root-reductive Lie algebras, Cartan subalgebras of the Lie algebra gl∞ were introduced and studied in [K.-H. Neeb, I. Penkov, Cartan subalgebras of gl∞, Canad. Math. Bull. 46 (2003) 597–616].In the present paper we refine and extend the results of [K.-H. Neeb, I. Penkov, Cartan subalgebras of gl∞, Canad. Math. Bull. 46 (2003) 597–616] to the case of a general root-reductive Lie algebra g. We prove that the Cartan subalgebras of g are the centralizers of maximal toral subalgebras and that they are nilpotent and self-normalizing. We also give an explicit description of all Cartan subalgebras of the simple Lie algebras sl∞, so∞, and sp∞.We conclude the paper with a characterization of the set of conjugacy classes of Cartan subalgebras of the Lie algebras gl∞, sl∞, so∞, and sp∞ with respect to the group of automorphisms of the natural representation which preserve the Lie algebra
Developments and retrospectives in Lie theory: geometric and analytic methods
No full textThis volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics. Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Geometric and Analytic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current research. Most of the workshops have taken place at leading public and private universities in California, though on occasion workshops have taken place in Oregon, Louisiana and Utah. Experts in representation theory/Lie theory from various parts of the Americas, Europe and Asia have given talks at these meetings. The workshop series is robust, and the meetings continue on a quarterly basis. Contributors to the Geometric and Analytic Methods volume: Y. Bahturin D. Miličić P. Bieliavsky K.-H. Neeb V. Gayral G. Ólafsson A. de Goursac E. Remm M. Goze W. Soergel J. Hilgert F. Spinnler A. Huckleberry M. Yakimov T. Kobayashi R. Zierau S. Mehdi
Characters of strongly generic irreducible Lie superalgebra representations.
No full text An explicit character formula is established for any strongly generic finite-dimensional irreducible [Formula: see text]-module, [Formula: see text] being an arbitrary finite-dimensional complex Lie superalgebra. This character formula had been conjectured earlier by Vera Serganova and the author for any generic irreducible finite-dimensional [Formula: see text]-module, i.e. such that its highest weight is far enough from the walls of the Weyl chambers. The condition of strong genericity, under which the conjecture is proved in this paper, is slightly stronger than genericity, but if in particular no simple component of [Formula: see text] is isomorphic to psq(n) for n ≥ 3 or to H(2k + 1) for k ≥ 2, strong genericity is equivalent to genericity. </jats:p
On the semi-infinite cohomology and categorification of the Boson-Fermion correspondence
No full textIn this thesis, we first examine the algebraic setting for the semi-infinite cohomology of a Lie algebra and then discuss the realization of semi-infinite cohomology by means of quantum groups. Next, we introduce the original bosonfermion correspondence and its categorification introduced by Frenkel, Penkov and Serganova. We then use the construction to categorify the Weyl algebra and Clifford algebra and their corresponding identities. Finally, we suggest possible future directions for these two topics.</p
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Influence of MoO₃ and ZrO₂ on the crystallization of fluor-mica fusion-cast ceramics
No full textNucleation and crystallization behavior of fluor-mica fusion-cast ceramics has been investigated. By contrast to oxide glasses, fusioncast ceramics based on potassium or barium fluor micas display a strong tendency to volume nucleation. For some specific compositions belonging to the latter group, the addition of MoO₃ and ZrO₂ has been studied. MoO₃ was selected because it is known to promote homogeneous nucleation by lowering the surface energy difference between melt and crystals, and ZrO₂ was selected because it is a classical nucleation catalyst in many glass-ceramic Systems. It is shown that both additives substantially reduce the crystallization rates and also cause concomitant changes in the resulting ceramic microstructures. Both effects are interpretated as a consequence of increased melt viscosity. An effect of nucleus formation promoted by MoO₃ is not observed
Borel subalgebras of gl(oo)
No full textThe paper is aself-contained statement of results and examples. Proofs willappear elsewhere
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