Representation Theory Seminar
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Thu, 15/10/2009 14:30 |
Petter Bergh (NTNU Trondheim) |
Representation Theory Seminar  |
L3 |
| This is joint work with Steffen Oppermann. A cluster category is obtained from the bounded derived category of a hereditary algebra, by forming the orbit category with respect to the suspension and the Auslander-Reiten translate. We study the complexity between objects in this triangulated category, and show the following: the maximal complexity occurring is either one, two or infinite, depending on whether the original algebra is of finte, tame or wild representation type. Moreover, we show that the complexity of a module over a tame cluster tilted algebra is at most one. | |||
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Thu, 22/10/2009 14:30 |
Andrzej Skowronski (Torun, Poland) |
Representation Theory Seminar |
L3 |
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Thu, 29/10/2009 14:30 |
John Murray (Maynooth (Ireland)) |
Representation Theory Seminar |
L3 |
| (Joint with Harald Ellers, Allegheny College, PA, USA) Carter and Payne constructed homomorphisms between Specht modules for the symmetric groups, based on moving boxes of the same residue in the associated partition diagrams. We study the special case of a one-box-shift. In particular, we give a lower bound for the Jantzen submodule of the codomain that contains the image. | |||
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Thu, 05/11/2009 14:30 |
Erik Darpo (Oxford/Uppsala) |
Representation Theory Seminar |
L3 |
| The transformation algebra of an algebra A is the subalgebra of the algebra of linear endomorphisms of A generated by all left and right multiplications with elements in A. It was introduced by Albert as a part of an effort to create a unified structure theory for non-associative algebras. One problem with the transformation algebra is that it is a very crude invariant for general algebras. In the talk, I shall suggest a way to compensate for this and show that by adding certain information, the transformation algebra can be used to give a complete picture of the category of unital division algebras of fixed (finite) dimension over a field. | |||
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Thu, 19/11/2009 14:30 |
Juergen Mueller (Aachen) |
Representation Theory Seminar |
L3 |
| Let G be a finite group, let A be a prime block of G having an abelian defect group D, let N be the normaliser in G of D, and let B be the Brauer correspondent of A. Then the abelian defect group conjecture says that the bounded derived categories of the module categories of A and B equivalent as triangulated categories. Although this conjecture is in the focus of intensive studies since almost two decades now, it has only been verified for certain cases and a general proof seems to be out of sight. In this talk, we briefly introduce the notions to state the abelian defect group conjecture, report on the current state of knowledge, and on the strategies to prove it for explicit examples. Then we show how these strategies are pursued and combined with techniques from computational representation theory to prove the abelian defect group conjecture for the sporadic simple Harada-Norton group; this is joint work with Shigeo Koshitani. | |||
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Thu, 26/11/2009 14:30 |
Anne Shepler (Denton, Texas and RWTH, Aachen) |
Representation Theory Seminar |
L3 |
| Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a critical role. We explore this structure for a finite group G acting on an algebra S by automorphisms. We capture the group together with its action with the natural semi-direct product, S#G, known as the "skew group algebra" or "smash product algebra". For example, when G acts linearly on a complex vector space V, it induces an action on the symmetric algebra S(V), a polynomial ring. The semi-direct product S(V)#G is a surrogate for the ring of invariant polynomials on V; it serves as the coordinate ring for the orbifold arising from the action of G on V. Deformations of this skew group algebra S(V)#G play a prominent role in representation theory. Such deformations include graded Hecke algebras (originally defined independently by Drinfeld and by Lusztig), symplectic reflection algebras (investigated by Etingof and Ginzburg in the study of orbifolds), and rational Cherednik algebras (introduced to solve Macdonald's inner product conjectures). We explore the graded Lie structure (or Gerstenhaber bracket) of the Hochschild cohomology of skew group algebras with an eye toward deformation theory. For abelian groups acting linearly, this structure can be described in terms of inner products of group characters. (Joint work with Sarah Witherspoon.) | |||
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Thu, 03/12/2009 14:30 |
Ernst Dieterich (Uppsala) |
Representation Theory Seminar |
L3 |
