Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/repns/notes 2014-15/03 generalities finite.pdf] 1. Subrepresentations, complete reducibility, unitarization 2. Dual/contragredient representations 3. Regular and biregular representations L(G) 4. Schur’s lemma 5. Central characters of irreducibles 6. Tensor products of repres...

a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...

A Fock space is introduced which admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimenisonal tilting and irreducible characters for the Lie superalgebra osp(2|2n). We also determine all the composition factors for the symmetric tensors of the natural osp...

Vogan has conjectured that a family of cohomologically induced modules exhaust the unitary dual of U(p, q) for certain kinds of integral infinitesimal characters. In this expository note (which is substantially a transcript of a talk given at the 1997 Seattle conference on the representation theory of real and p-adic groups) we recall the definition of the relevant modules, describe an approach...

Aspergillus section Nidulantes includes species with striking morphological characters, such as biseriate conidiophores with brown-pigmented stipes, and if present, the production of ascomata embedded in masses of Hülle cells with often reddish brown ascospores. The majority of species in this section have a sexual state, which were named Emericella in the dual name nomenclature system. In the ...

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...

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The influence of VAM fungi and bacterial biofertilizer (BBF) with 50% reduction in the recommended dose of (N and P) chemical fertilizers on leaf quality traits of mulberry variety (S-13) and its impact on silkworm (PM ? NB4D2) growth and cocoon characters were studied under semi-arid conditions. Four different treatments were imposed i.e., T1: Control (only 100% NPK); T2: VAM (50% cut in P); ...