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Supersymmetry |
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| in Mathematics |
| & Physics |
February 6-7, 2010 at UCLA |
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Download Program: PDF
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SATURDAY - February 6, 2010
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Opening remarks by Varadarajan |
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[Speaker] - Rita Fioresi | University of Bologna |
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[Speaker] - Jeffrey Rabin | UCSD |
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[Speaker] - Albert Schwartz | UC Davis |
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Catered Lunch |
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[Speaker] - Maria Lledo | University of Valencia |
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Coffee Break |
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[Speaker] - Hadi Salmasian | University of Ottawa |
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[Speaker] - Sergio Ferrara | CERN |
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Dinner |
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SUNDAY - February 7, 2010
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[Speaker] - Vera Serganova | UC Berkeley |
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Coffee Break |
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[Speaker] - Ian Musson | University of Wisconsin-Milwaukee |
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[Speaker] - Claudio Carmeli | University of Genova
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Lunch |
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TITLES
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| C. Carmeli |
University of Genova
Induced representations of super Lie groups. |
| S. Ferrara |
CERN
Extremal Black Holes in N=8 Supergravity and the Exceptional group E7,7. |
| R. Fioresi |
University of Bologna
Chevalley Supergroups. |
| M. Lledo |
University of Valencia
On the quantization of Minkowski and conformal superspaces. |
| I. Musson |
University of Wisconsin-Milwaukee
Combinatorics of Character Formulas for the Lie Superalgebra gl(m, n). |
| J. Rabin |
UCSD
Geometry of Dual Pairs of Complex Supercurves. |
| H. Salmasian |
University of Ottawa
Unitary representations of nilpotent super Lie groups. |
| A. Schwarz |
UC Davis
Maximally supersymmetric gauge theories. |
| V. Serganova |
UC Berkeley
Kac-Wakimoto conjecture about superdimension of an irreducible representation of a classical Lie superalgebra. |
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ABSTRACTS
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Claudio Carmeli: Induced Representations of Super Lie Groups
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The category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs. We review this basic fact, and we apply it to outline a general theory of induced rep- resentations of SLG. The basic results of the theory (like the induction in stages theorem) are presented and a possible formulation of a super imprimitivity theorem is discussed. As a an application, we give a detailed exposition of the special induction functor. In this case the SLG G is a super semi direct product and the inducing subgroup has the same odd part as G. The example of the super Poincare’ group is briefly sketched. |
Sergio Ferrara: Extremal Black Holes in N=8 Supergravity and the Exceptional group E7,7
We describe extremal black hole solutions of four dimensional supergravities with different amount of supersymmetry. Attractor BPS and non-BPS solutions are considered and the role of the exceptional group E7,7 for their Bekenstein Hawking entropy-area formula outlined. We describe extremal black hole solutions of four dimensional supergravities with different amount of supersymmetry. Attractor BPS and non-BPS solutions are considered and the role of the exceptional group E7,7 for their Bekenstein Hawking entropy-area formula outlined. |
Rita Fioresi: Chevalley Supergroups
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In the framework of algebraic supergeometry, we construct the scheme-theoretic supergeometric analogue of Chevalley groups associated to Lie superalgebras of classical type. This provides a unifying and characteristic free approach to most of the algebraic supergroups considered so far in literature and an effective method to construct new ones, namely the supergroups associated to the exceptional Lie superalgebras. |
Maria Lledo: On the quantization of Minkowski and conformal superspaces.
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We propose a deformed, quantum version of Minkowski superspace seen as the big cell inside a conformal superspace. The Poincar and conformal supergroups become also deformed as quantum supergroups, so they become themselves non commutative superspaces. The group law nevertheless remains the same, so the physical symmetries are not deformed. |
Ian Musson: Combinatorics of Character Formulas for the Lie Superalgebra gl(m, n)
Let g be the Lie superalgebra gl(m, n). Algorithms for computing the com- position factors and multiplicities of Kac modules for g were given by V.V. Serganova, [Ser96] and by J. Brundan [Bru03]. We give a combinatorial proof of the equivalence between the two algo- rithms. The proof uses weight and cap diagrams introduced by Brundan and C. Stroppel, and cancelations between paths in a graph G defined using these diagrams. Each vertex of G corresponds to a highest weight of a finite dimen- sional simple module, and each edge is weighted by a nonnega- tive integer. If E is the subgraph of G obtained by deleting all edges of positive weight, then E is the graph that describes non-split extensions between simple highest weight modules. We also give a procedure for finding the composition factors of any Kac module, without cancelation. This is joint work with Vera V. Serganova.
References
[Bru03] J. Brundan, Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra gl(m—n), J. Amer. Math. Soc. 16 (2003), no. 1, 185231 (electronic). MR 1937204 (2003k:17007)
[Ser96] V. Serganova, Kazhdan-Lusztig polynomials and character formula for the Lie superalgebra gl(m—n), Selecta Math. (N.S.) 2 (1996), no. 4, 607651. MR 1443186 (98f:17007) |
Jeffrey M. Rabin: Geometry of Dual Pairs of Complex Supercurves
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The naive generalization to supergeometry of the concept of Riemann surface would be a (smooth) supercurve: a complex supermanifold of dimension 1—1. These come in dual pairs X, Y such that the points of one represent the irreducible divisors on the other. Super Riemann surfaces, introduced by string theorists, are self-dual supercurves, the special case where X=Y. I’ll survey some aspects of the geometry of supercurves, mainly revolving around relationships between line bundles and differentials on a pair of dual supercurves. Illustrative examples include super elliptic curves. |
Hadi Salmasian: Unitary representations of nilpotent super Lie groups
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In the fifties Kirillov showed that the unitary dual of a nilpotent Lie group has a geometric description in terms of quantization of coadjoint orbits. In this talk I explain how to generalize Kirillov’s result to nilpotent super Lie groups. In the super case one observes that for nilpotent super Lie groups there exists a bijective correpondence between representations and ”nonneg- ative” coadjoint orbits. As a result, one observes that usually a nilpotent super Lie group has ”fewer” irreducible representations than its own even part. |
Albert Schwarz: Maximally supersymmetric gauge theories
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The talk will be devoted to supersymmetric deformations of ten-dimensional supersymmetric Yang-Mills theory and of dimensional reductions of this theory. The talk is based on joint papers with M. Movshev. |
Vera Serganova: Kac-Wakimoto conjecture about superdimension of an irreducible representation of a classical Lie superalgebra
In 1994 Kac and Wakimoto conjectured that a superdimension of a finite-dimensional irreducible representation is not zero if and only if the representation has maximal degree of atypicality (the degree of atypicality is an important discrete invariant of a representation). We will give a proof of this conjecture for orthosymplectic and general linear superalgebra.
The proof is based on calculation of cohomology of line bundles on certain partial flag supervarieties obtained jointly with C. Gruson in the orthosymplectic case and on my joint work with M. Duflo. |
POSTER ABSTRACTS
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A star product on the big cell of the supergrassmannian manifold Gr(2|0, 4|1)
Dalia B. Cervantes Cabrera
Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico
daliac@nucleares.unam.mx
Using the algebraic nature of the Grassmanian supermanifold, we define a star product for the big cell. We express it in terms of the standard coordinates of Minkowski superspace.
Super theta functions
Stephen Kwok
Department of Mathematics, UCLA
sdkwok@math.ucla.edu
Levin defines super theta functions on 1|1 super elliptic curves. While classical theta functions are sections of a line bundle, their super analogues are sections of a different type of object--a P-invertible sheaf.
We relate the super theta functions to representations of the super Heisenberg group, and give a new construction of Manin's "P-projective space" associated to P-invertible sheaves.
Charge Orbits and Moduli Spaces of Black Hole Attractors
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Alessio Marrani
CERN, Geneva
alessio.marrani@lfn.infn.it,
The role of the orbits of the representation space of charges, as well as of the moduli spaces of attractor solutions, will be discussed within the theory of supergravity in diverse space-time dimensions. A detailed treatment of theories with symmetric scalar manifolds will be given. |
PARTICIPANTS
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Izuerita ARANDA
Catholic University at San Andres
Donald BABBITT
UCLA
Itzhak BARS
USC
Claudio CARMELI
University of Genova
Gianni CASSINELLI
University of Genova
Nerina CASSINELLI
University of Genova
Lauren CASTON
Rand
Dalia CERVANTES
University of Valencia
Babette DALTON
UCLA
Trond DIGERNES
University of Trondheim/UCLA
Sergio FERRARA
CERN
Rita FIORESI
University of Bologna
Yaron HADAD
University of Arizona
Stephen KWOK
UCLA |
Marian LLEDO
University of Valencia
Thomas LOVE
CSU at Dominguez Hills
Alessio MARRANI
CERN
Ian MUSSON
University of Wisconsin-Milwaukee
Jeffrey RABIN
UCSD
Hadi SALMASIAN
University of Ottawa
Albert SCHWARZ
UC Davis
Vera SERGANOVA
UC Berkeley
David TAYLOR
UCLA
Veeravalli VARADARAJAN
UCLA
Jukka VIRTANEN
UCLA
David WEISBART
UCLA
Martin WOLD
University of Trondheim/UCLA |
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