A basis theorem for the degenerate affine oriented Brauer-Clifford supercategory

We introduce the oriented Brauer-Clifford and degenerate affine oriented Brauer-Clifford supercategories. These are diagrammatically defined monoidal supercategories which provide combinatorial models for certain natural monoidal supercategories of supermodules and endosuperfunctors, respectively, for the Lie superalgebras of type Q. Our main results are basis theorems for these diagram supercategories. We also discuss connections and applications to the representation theory of the Lie superalgebra of type Q.Comment: 37 pages, many figures. Version 3 replaces the partial results from the previous versions with a proof by the first author of a basis theorem for cyclotomic quotients at all levels. Various other minor corrections and revisions were mad

Regular Polytopes

In the last proposition of the Elements Euclid proved that there are only five regular polyhedra, namely the tetrahedron, octahedron, icosahedron, cube, and dodecahedron. To show there can be no more than five he used the fact that in a polyhedra, the sum of the interior angles of the faces which meet at each vertex must be less than 360

On blocks of Deligne's category Rep(S_t)

Recently P. Deligne introduced the tensor category Rep(S_t) (for t not necessarily an integer) which in a certain precise sense interpolates the categories Rep(S_d) of representations of the symmetric groups S_d. In this paper we describe the blocks of Deligne's category Rep(S_t).Comment: 43 pages, final version, includes an added appendix as well as other modifications recommended by the refere

Pyrethroids inhibit K2P channels and activate sensory neurons: basis of insecticide-induced paraesthesias

Pyrethroid insecticides are widely used for pest control in agriculture or in human public health commonly as a topical treatment for scabies and head lice. Exposure to pyrethroids such as permethrin or tetramethrin (TM) causes sensory alterations such as transient pain, burning, stinging sensations, and paraesthesias. Despite the well-known effects of pyrethroids on sodium channels, actions on other channels that control sensory neuron excitability are less studied. Given the role of 2-pore domain potassium (K2P) channels in modulating sensory neuron excitability and firing, both in physiological and pathological conditions, we examined the effect of pyrethroids on K2P channels mainly expressed in sensory neurons. Through electrophysiological and calcium imaging experiments, we show that a high percentage of TM-responding neurons were nociceptors, which were also activated by TRPA1 and/or TRPV1 agonists. This pyrethroid also activated and enhanced the excitability of peripheral saphenous nerve fibers. Pyrethroids produced a significant inhibition of native TRESK, TRAAK, TREK-1, and TREK-2 currents. Similar effects were found in transfected HEK293 cells. At the behavioral level, intradermal TM injection in the mouse paw produced nocifensive responses and caused mechanical allodynia, demonstrating that the effects seen on nociceptors in culture lead to pain-associated behaviors in vivo. In TRESK knockout mice, pain-associated behaviors elicited by TM were enhanced, providing further evidence for a role of this channel in preventing excessive neuronal activation. Our results indicate that inhibition of K2P channels facilitates sensory neuron activation and increases their excitability. These effects contribute to the generation of paraesthesias and pain after pyrethroid exposure