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Bar complexes and extensions of classical exponential functors

Antoine Touzé (2014)

Annales de l’institut Fourier

We compute Ext-groups between classical exponential functors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and bridges these Ext-groups with the homology of Eilenberg-Mac Lane spaces.This article completes earlier results of the author, and provides an alternative approach to classical Ext-computations in the category of strict polynomial functors over fields. We also obtain significant Ext-computations for strict polynomial functors...

Bar-invariant bases of the quantum cluster algebra of type A 2 ( 2 )

Xueqing Chen, Ming Ding, Jie Sheng (2011)

Czechoslovak Mathematical Journal

We construct bar-invariant ℤ [ q ± 1 / 2 ] -bases of the quantum cluster algebra of the valued quiver A 2 ( 2 ) , one of which coincides with the quantum analogue of the basis of the corresponding cluster algebra discussed in P. Sherman, A. Zelevinsky: Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Moscow Math. J., 4, 2004, 947–974.

Base change for Bernstein centers of depth zero principal series blocks

Thomas J. Haines (2012)

Annales scientifiques de l'École Normale Supérieure

Let  G be an unramified group over a p -adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for  G and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with Γ 1 ( p ) -level structure initiated by M. Rapoport and the author in [15].

Bilinear forms for SL(2,q), An and similar groups.

Alexandre Turull (1992)

Publicacions Matemàtiques

The set of invariant symmetric bilinear forms on irreducible modules over fields of characteristic zero for certain groups is studied. Results are obtained under the presence in a finite group of elements of order four whose square is central. In particular, we find that the relevant modules for the groups mentioned in the title always accept an invariant symmetric bilinear form under which the module admits an orthonormal basis.

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