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Arxiv.org
by Eric Marberg
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Diaconis and Isaacs define a supercharacter theory for algebra groups over a finite field by constructing certain unions of conjugacy classes called superclasses and certain reducible characters called supercharacters. This work investigates the properties of algebra subgroups $H\subset G$ which are unions of some set of the superclasses of $G$; we call such subgroups supernormal. After giving a few useful equivalent formulations of this definition, we show that products of supernormal...
Source: http://arxiv.org/abs/1005.4150v4
Arxiv.org
by Jean-Louis Colliot-Thélène; Claire Voisin
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Building upon the Bloch-Kato conjecture in Milnor K-theory, we relate the third unramified cohomology group with Q/Z coefficients with a group which measures the failure of the integral Hodge conjecture in degree 4. As a first consequence, a geometric theorem of the second-named author implies that the third unramified cohomology group with Q/Z coefficients vanishes on all uniruled threefolds. As a second consequence, a 1989 example by Ojanguren and the first named author implies that the...
Source: http://arxiv.org/abs/1005.2778v2
Arxiv.org
by Jorma Louko; Eric Martinez-Pascual
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We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a rigging map that is motivated by group averaging but has a resolution finer than what can be peeled off from the formally divergent contributions to the averaging integral. Three cases emerge, depending on the asymptotics of the rescaling function: (i)...
Source: http://arxiv.org/abs/1107.1092v2
Arxiv.org
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In this paper, we study dimensions of some varieties, that were introduced recently by Kisin in order to prove modularity of some Galois representations. In fact, we mainly consider a special case for which we obtain an estimation of the dimension we are interested in. Then, based on this result, we state a conjecture for the general case.
Source: http://arxiv.org/abs/1005.2394v2
Arxiv.org
by Alexandre Bouayad
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Interpolating Langlands Quantum Groups of Rank 1 -- We study a certain family, parameterized by an positive integer g, of double deformations of the envelopping algebra U(sl2), in the spirit of arXiv:0809.4453. We prove that each of these double deformations simultaneously deforms two rank 1 quantum groups. We show this interpolating property explains the Langlands duality for the representations of the quantum groups in rank 1. Hence we prove a conjecture of arXiv:0809.4453 in this case : we...
Source: http://arxiv.org/abs/1107.1992v1