Related papers: Modular Representations and Indicators for Bismash…

Bernstein, Frenkel and Khovanov have constructed a categorification of tensor products of the standard representation of $\mathfrak{sl}_2$ using singular blocks of category $\mathcal{O}$ for $\mathfrak{sl}_n$. In earlier work, we construct…

The computation of the Brauer group BM of modified supergroup algebras is perfomed, yielding, in particular, the computation of the Brauer group of all finite-dimensional triangular Hopf algebras when the base field is algebraically closed…

The Brauer algebra has a basis of diagrams and these generate a monoid $H$ consisting of scalar multiples of diagrams. Following a recent paper by Kudryavtseva and Mazorchuk, we define and completely determine three types of conjugation in…

The purpose of the present paper is to investigate a hypergroup arising from irreducible characters of a compact group G and a closed subgroup of G with finite index. The convolution of this hypergroup is introduced by inducing irreducible…

Frobenius-Schur indicators (or indicators for short) of objects in pivotal monoidal categories were defined and formulated by Ng and Schauenburg in 2007. In this paper, we introduce and study an analogous formula for indicators in the dual…

We prove that Alvis-Curtis duality preserves the Frobenius-Schur indicators of characters of connected reductive groups of Lie type with connected center. This allows us to extend a result of D. Prasad which relates the Frobenius-Schur…

Let $k$ be a finitely generated field of characteristic $p>0$ and $X$ a smooth and proper scheme over $k$. Recent works of Cadoret, Hui and Tamagawa show that, if $X$ satisfies the $\ell$-adic Tate conjecture for divisors for every prime…

The authors continue a series of articles studying certain unitary representations of the Richard Thompson groups $F,T,V$ called Pythagorean. They all extend to the Cuntz algebra $\mathcal{O}$ and conversely all representations of…

We study the decomposition of tensor products between a Steinberg module and a costandard module, both as a module for the algebraic group $G$ and when restricted to either a Frobenius kernel $G_r$ or a finite Chevalley group…

We prove a strengthening of Brauer's height zero conjecture for principal 2-blocks with Galois automorphisms. This requires a new extension of the It\^o--Michler theorem for the prime~2, again with Galois automorphisms. We close, this time…

M. Kiyota, T. Okuyama and T. Wada recently proved that each 2-block of a finite symmetric group contains a unique irreducible Brauer character that has height 0. We present a more conceptual proof of this result.

Mason and Ng have given a generalization to semisimple quasi-Hopf algebras of Linchenko and Montgomery's generalization to semisimple Hopf algebras of the classical Frobenius-Schur theorem for group representations. We give a simplified…

We study the structure of the finite-dimensional representations of $\mathfrak{sl}_2[t]$, the current Lie algebra type of $A_1$, which are obtained by taking tensor products of special Demazure modules. We show that these representations…

In "Frobenius Categories versus Brauer Blocks", Progress in Math. 274, we have introduced the Frobenius categories F over a finite p-group P, and we have associated to F - suitably endowed with some central k*-extensions - a "Grothendieck…

Coates, Fukaya, Kato, Sujatha and Venjakob come up with a procedure of attaching suitable characteristic element to Selmer groups defined over a non-commutative $p$-adic Lie extension, which is subsequently refined by Burns and Venjakob. By…

Let $p$ be a prime for which the congruence group $\Gamma_0(p)^*$ is of genus zero, and $j_p^*$ be the corresponding Hauptmodul. Let $f$ be a nearly holomorphic modular form of weight 1/2 on $\Gamma_0(4p)$ which satisfies some congruence…

Let $\Gamma$ be a discrete icc subgroup of PSL(2,R) of infinite covolume. and let M denote the quotient of the unit disc by $\Gamma$. We prove that a Toeplitz operator with $\Gamma$-invariant symbol f in C(M) is Brauer Fredholm if its…

For a torsion unit $u$ of the integral group ring $\mathbb{Z} G$ of a finite group $G$, and a prime $p$ which does not divide the order of $u$ (but the order of $G$), a relation between the partial augmentations of $u$ on the $p$-regular…

Let p be an odd prime and let L/k be a Galois extension of number fields whose Galois group is isomorphic to the dihedral group of order 2p. Let S be a finite set of primes of L which is stable under the action of Gal(L/k). The Lichtenbaum…

We present an approach of calculating the group of braided autoequivalences of the category of representations of the Drinfeld double of a finite dimensional Hopf algebra $H$ and thus the Brauer-Picard group of $H$-$\mathrm{mod}$. We…