Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.Comment: 32 page

Cohomology and Support Varieties for Lie Superalgebras II

In \cite{BKN} the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a detecting subalgebra coincides with the defect of the Lie superalgebra and the dimension of the support variety for a simple supermodule was conjectured to equal the atypicality of the supermodule. In this paper the authors compute the support varieties for Kac supermodules for Type I Lie superalgebras and the simple supermodules for $\mathfrak{gl}(m|n)$. The latter result verifies our earlier conjecture for $\mathfrak{gl}(m|n)$. In our investigation we also delineate several of the major differences between Type I versus Type II classical Lie superalgebras. Finally, the connection between atypicality, defect and superdimension is made more precise by using the theory of support varieties and representations of Clifford superalgebras.Comment: 28 pages, the proof of Proposition 4.5.1 was corrected, several other small errors were fixe

Breeding Yellow-flowered Alfalfa for Combined Wildlife Habitat and Forage Purposes

The objectives of our research were to: • evaluate a wide array of alfalfa germplasm containing varied levels of M. sativa ssp. falcata for traits related to suitability for stockpiling and nesting cover for game birds, •compare yellow-flowered cultivars and germplasms to conventional hay- and pasture-type cultivars for forage yield and quality in a delayed single-harvest / production system, and • develop, by phenotypic selection, one or more synthetic cultivars of yellow-flowered alfalfa that would have high forage yield, tolerance to potato leafhopper yellowing, prolonged flowering, and good leaf retention under a stockpiling management system until mid-July

Alfalfa Cultivar Yield Test for South Dakota: 1993 Report

Public and commercial breeding programs have produced many alfalfa cultivars in the last 15 years. That makes selecting the proper cultivar for your needs no easy task, for you should have yield information from several South Dakota locations before choosing. The Alfalfa Cultivar Yield Test reports relative forage production characteristics for available cultivars and experimental lines at several locations in South Dakota

Alfalfa Cultivar Yield Test for South Dakota: 1996 Report

The South Dakota Alfalfa Cultivar Yield Test reports relative forage production characteristics for available alfalfa cultivars at several locations in South Dakota. Cultivars are entered in the Yield Test by seed companies and public breeders at their own discretion. A list of alfalfa cultivars and the companies which market them is in the Appendix at the end of this bulletin

Comparison of fatty acid profile in lamb meat and baby food based on lamb meat

The aim of this study was to compare the fatty acid (FA) profile of fresh lamb meat with those of baby foods based on lamb meat. For this purpose, samples of commercial homogenized (HO) and lyophilized (LIO) baby food based on lamb meat and fresh lamb meat (FM) were analyzed for their FA composition. All fatty acids, except for oleic acid and conjugated linoleic acid (CLA), differed among the three baby products tested. The sum of omega-6 FA and the ratio omega 6/omega 3 FA were lower in FM and LIO meat compared to HO samples. The content of total PUFA n-3 was the highest in FM, because of its highest content of C18:3 n3, EPA, DPA and DHA compared to LIO and HO baby food. The content of arachidonic acid was more than 6-fold higher in FM compared to LIO and HO. This study evidenced the possibility of enhancing the FA profile of commercial baby food based on lamb meat by using meat with healthier FA profile