ترغب بنشر مسار تعليمي؟ اضغط هنا

Modular Representations and Indicators for Bismash Products

109   0   0.0 ( 0 )
 نشر من قبل Susan Montgomery
 تاريخ النشر 2012
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We introduce Brauer characters for representations of the bismash products of groups in characteristic p > 0, p not 2 and study their properties analogous to the classical case of finite groups. We then use our results to extend to bismash products a theorem of Thompson on lifting Frobenius-Schur indicators from characteristic p to characteristic 0



قيم البحث

اقرأ أيضاً

In this paper we introduce the notion of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence associated with Hecke algebras is representation stable.
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 a positive ch aracteristic analogue using blocks of representations of $mathfrak{sl}_n$ over a field $textbf{k}$ of characteristic $p > n$, with zero Frobenius character, and singular Harish-Chandra character. In the present paper, we extend these results and construct a categorical $mathfrak{sl}_k$-action, following Sussans approach, by considering more singular blocks of modular representations of $mathfrak{sl}_n$. We consider both zero and non-zero Frobenius central character. In the former setting, we construct a graded lift of these categorifications which are equivalent to a geometric construction of Cautis, Kamnitzer and Licata. We establish a Koszul duality between two geometric categorificatons constructed in their work, and resolve a conjecture of theirs. For non-zero Frobenius central characters, we show that the geometric approach to categorical symmetric Howe duality by Cautis and Kamnitzer can be used to construct a graded lift of our categorification using singular blocks of modular representations of $mathfrak{sl}_n$.
We use the isomorphisms between the $R$-matrix and Drinfeld presentations of the quantum affine algebras in types $B$, $C$ and $D$ produced in our previous work to describe finite-dimensional irreducible representations in the $R$-matrix realization. We also review the isomorphisms for the Yangians of these types and use Gauss decomposition to establish an equivalence of the descriptions of the representations in the $R$-matrix and Drinfeld presentations of the Yangians.
The core of a finite-dimensional modular representation $M$ of a finite group $G$ is its largest non-projective summand. We prove that the dimensions of the cores of $M^{otimes n}$ have algebraic Hilbert series when $M$ is Omega-algebraic, in the sen se that the non-projective summands of $M^{otimes n}$ fall into finitely many orbits under the action of the syzygy operator $Omega$. Similarly, we prove that these dimension sequences are eventually linearly recursive when $M$ is what we term $Omega^{+}$-algebraic. This partially answers a conjecture by Benson and Symonds. Along the way, we also prove a number of auxiliary permanence results for linear recurrence under operations on multi-variable sequences.
We study the category of representations of $mathfrak{sl}_{m+2n}$ in positive characteristic, whose p-character is a nilpotent whose Jordan type is the two-row partition (m+n,n). In a previous paper with Anno, we used Bezrukavnikov-Mirkovic-Rumynins theory of positive characteristic localization and exotic t-structures to give a geometric parametrization of the simples using annular crossingless matchings. Building on this, here we give combinatorial dimension formulae for the simple objects, and compute the Jordan-Holder multiplicities of the simples inside the baby Vermas (in special case where n=1, i.e. that a subregular nilpotent, these were known from work of Jantzen). We use Cautis-Kamnitzers geometric categorification of the tangle calculus to study the images of the simple objects under the [BMR] equivalence. The dimension formulae may be viewed as a positive characteristic analogue of the combinatorial character formulae for simple objects in parabolic category O for $mathfrak{sl}_{m+2n}$, due to Lascoux and Schutzenberger.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا