Steinberg modules and Donkin pairs

We prove that in positive characteristic a module with good filtration for a group of type E6 restricts to a module with good filtration for a subgroup of type F4. (Recall that a filtration of a module for a semisimple algebraic group is called good if its layers are dual Weyl modules.) Our result confirms a conjecture of Brundan for one more case. The method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, in characteristic not 2, with a computer-aided variation on the old method of Donkin.Comment: 16 pages; proof of Brundan's conjecture adde

Category O over a deformation of the symplectic oscillator algebra

We discuss the representation theory of $H_f$, which is a deformation of the symplectic oscillator algebra $sp(2n) \ltimes h_n$, where $h_n$ is the ((2n+1)-dimensional) Heisenberg algebra. We first look at a more general setup, involving an algebra with a triangular decomposition. Assuming the PBW theorem, and one other hypothesis, we show that the BGG category $\mathcal{O}$ is abelian, finite length, and self-dual. We decompose $\mathcal{O}$ as a direct sum of blocks \calo(\la), and show that each block is a highest weight category. In the second part, we focus on the case $H_f$ for $n=1$, where we prove all these assumptions, as well as the PBW theorem.Comment: 42 pages, LaTeX, 11pt; Typos removed, references added, presentation improved, minor corrections and additions, Section 16 modified, and Standing Assumption added in Section 17; Final form, to appear in the Journal of Pure and Applied Algebr

How to Change the Weight of Rare Events in Decisions from Experience

When making risky choices, two kinds of information are crucial: outcome values and outcome probabilities. Here, we demonstrate that the juncture at which value and probability information is provided has a fundamental effect on choice. Across four experiments involving 489 participants, we compare two decision making scenarios: one where value information is revealed during sampling (Standard), and one where value information is revealed after sampling (Value-Ignorance). On average, participants made riskier choices when value information was provided after sampling. Moreover, parameter estimates from a hierarchical Bayesian implementation of cumulative prospect theory suggested that participants overweighted rare events when value information was absent during sampling, but showed no overweighting in the Standard condition. This suggests that the impact of rare events on choice relies crucially on the timing of probability and value integration. We provide paths towards mechanistic explanations of our results based on frameworks which assume different underlying cognitive architectures

Effect of Leucaena leucocephala, as a protein source in a total mixed ration, on milk yield and composition of Saanen milk goats

This study examined the effects of diets with two protein sources (oilseed cake meal (OSCM) and Leucaena leucocephala hay) on the performance of lactating goats that were fed a total mixed ration (TMR). Thirty Saanen milk goats were divided into two groups, which were fed one of the two TMRS, with or without Leucaena hay at 25% of the DM. The TMRs were formulated to be iso-nitrogenous, iso-energetic and iso-neutral detergent fibre, while using two sources of crude protein, namely i) Leucaena hay; and ii) oilseed cake meal OSCM from soybean, sunflower, and cottonseed. No significant differences were revealed in body condition score, bodyweight change, milk yield and milk composition, such as milk fat (%), milk lactose (%), somatic cell count (x 103 cells/mL) and milk protein (%) during the entire lactation period. In contrast, goats fed the TMR with Leucaena hay had a lower milk urea nitrogen (mg nitrogen/dL) level than those fed the control diet (with OSCM). It was concluded that replacing a proportion of oilseed cake meal with Leucaena in Saanen milk goats fed TMR does not negatively influence milk production and composition.Keywords: fodder tree, oilseed cake, protein concentrate, somatic cell coun

Carter-Payne homomorphisms and Jantzen filtrations

We prove a q-analogue of the Carter-Payne theorem in the case where the differences between the parts of the partitions are sufficiently large. We identify a layer of the Jantzen filtration which contains the image of these Carter-Payne homomorphisms and we show how these homomorphisms compose.Comment: 30 page

Homomorphisms and Higher Extensions for Schur algebras and symmetric groups

This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext groups in the two categories, and discuss those cases where explicit results have been determined

Sub-post offices and high street revitalisation: lessons from the experience of grant assistance to sub-post offices in deprived urban areas of the UK

Post Offices (POs) are essential service providers within deprived urban areas. This paper explores some lessons from the impact of grant assistance to sub-post offices (SPOs) in deprived urban areas of England and Scotland which are relevant to contemporary policy initiatives to revive high streets. Utilising longitudinal data to explore whether government grant assistance has made a difference in enabling the survival and development of assisted SPOs, it also considers their role in maintaining and developing shops and services in deprived urban neighbourhoods. The inter-relationship of SPOs with their local economies and communities is explored, including external influences such as competition and complementarity and internal influences relating to the evolving role of SPOs in the early 21st century. A central theme is the apparent paradox between the UK Government’s desire to maintain SPOs as essential service providers and catalysts for other ‘high street’ services within deprived urban areas, whilst opening their core services up to increasing levels of competition. Key Words: Post Offices, Retail, High Street Services, Urban, Regeneration, Deprivatio

Super duality and irreducible characters of ortho-symplectic Lie superalgebras

We formulate and establish a super duality which connects parabolic categories $O$ between the ortho-symplectic Lie superalgebras and classical Lie algebras of $BCD$ types. This provides a complete and conceptual solution of the irreducible character problem for the ortho-symplectic Lie superalgebras in a parabolic category $O$, which includes all finite-dimensional irreducible modules, in terms of classical Kazhdan-Lusztig polynomials.Comment: 30 pages, Section 5 rewritten and shortene