Vertices of simple modules of symmetric groups labelled by hook partitions

In this article we study the vertices of simple modules for the symmetric groups in prime characteristic $p$. In particular, we complete the classification of the vertices of simple $S_n$-modules labelled by hook partitions

Quasi-hereditary structure of twisted split category algebras revisited

Let $k$ be a field of characteristic $0$, let $\mathsf{C}$ be a finite split category, let $\alpha$ be a 2-cocycle of $\mathsf{C}$ with values in the multiplicative group of $k$, and consider the resulting twisted category algebra $A:=k_\alpha\mathsf{C}$. Several interesting algebras arise that way, for instance, the Brauer algebra. Moreover, the category of biset functors over $k$ is equivalent to a module category over a condensed algebra $\varepsilon A\varepsilon$, for an idempotent $\varepsilon$ of $A$. In [2] the authors proved that $A$ is quasi-hereditary (with respect to an explicit partial order $\le$ on the set of irreducible modules), and standard modules were given explicitly. Here, we improve the partial order $\le$ by introducing a coarser order $\unlhd$ leading to the same results on $A$, but which allows to pass the quasi-heredity result to the condensed algebra $\varepsilon A\varepsilon$ describing biset functors, thereby giving a different proof of a quasi-heredity result of Webb, see [26]. The new partial order $\unlhd$ has not been considered before, even in the special cases, and we evaluate it explicitly for the case of biset functors and the Brauer algebra. It also puts further restrictions on the possible composition factors of standard modules.Comment: 39 page

Signed Young Modules and Simple Specht Modules

By a result of Hemmer, every simple Specht module of a finite symmetric group over a field of odd characteristic is a signed Young module. While Specht modules are parametrized by partitions, indecomposable signed Young modules are parametrized by certain pairs of partitions. The main result of this article establishes the signed Young module labels of simple Specht modules. Along the way we prove a number of results concerning indecomposable signed Young modules that are of independent interest. In particular, we determine the label of the indecomposable signed Young module obtained by tensoring a given indecomposable signed Young module with the sign representation. As consequences, we obtain the Green vertices, Green correspondents, cohomological varieties, and complexities of all simple Specht modules and a class of simple modules of symmetric groups, and extend the results of Gill on periodic Young modules to periodic indecomposable signed Young modules.Comment: To appear in Adv. Math. 307 (2017) 369--416. Proposition 4.3 (F4), (F5) corrected, Lemma 4.9 adjusted accordingl

Vorticity of viscous electronic flow in graphene

In ultra-pure materials electrons may exhibit a collective motion similar to the hydrodynamic flow of a viscous fluid, the phenomenon with far reaching consequences in a wide range of many body systems from black holes to high-temperature superconductivity. Yet the definitive detection of this intriguing behavior remains elusive. Until recently, experimental techniques for observing hydrodynamic behavior in solids were based on measuring macroscopic transport properties, such as the "nonlocal" (or "vicinity") resistance, which may allow alternative interpretation. Earlier this year two breakthrough experiments demonstrated two distinct imaging techniques making it possible to "observe" the electronic flow directly. We demonstrate that a hydrodynamic flow in a long Hall bar (in the absence of magnetic field) exhibits a nontrivial vortex structure accompanied by a sign-alternating nonlocal resistance. An experimental observation of such unique flow pattern could serve a definitive proof of electronic hydrodynamics.Comment: 6 pages, 5 figure

A ghost algebra of the double Burnside algebra in characteristic zero

For a finite group $G$, we introduce a multiplication on the \QQ-vector space with basis \scrS_{G\times G}, the set of subgroups of $G\times G$. The resulting \QQ-algebra \Atilde can be considered as a ghost algebra for the double Burnside ring $B(G,G)$ in the sense that the mark homomorphism from $B(G,G)$ to \Atilde is a ring homomorphism. Our approach interprets \QQ B(G,G) as an algebra $eAe$, where $A$ is a twisted monoid algebra and $e$ is an idempotent in $A$. The monoid underlying the algebra $A$ is again equal to \scrS_{G\times G} with multiplication given by composition of relations (when a subgroup of $G\times G$ is interpreted as a relation between $G$ and $G$). The algebras $A$ and \Atilde are isomorphic via M\"obius inversion in the poset \scrS_{G\times G}. As an application we improve results by Bouc on the parametrization of simple modules of \QQ B(G,G) and also of simple biset functors, by using results by Linckelmann and Stolorz on the parametrization of simple modules of finite category algebras. Finally, in the case where $G$ is a cyclic group of order $n$, we give an explicit isomorphism between \QQ B(G,G) and a direct product of matrix rings over group algebras of the automorphism groups of cyclic groups of order $k$, where $k$ divides $n$.Comment: 41 pages. Changed title from "Ghost algebras of double Burnside algebras via Schur functors" and other minor changes. Final versio

Information Flow Analysis of Level 4 Payload Processing Operations

The Level 4 Mission Sequence Test (MST) was studied to develop strategies and recommendations to facilitate information flow. Recommendations developed as a result of this study include revised format of the Test and Assembly Procedure (TAP) document and a conceptualized software based system to assist in the management of information flow during the MST

Information and Beliefs in a Repeated Normal-form Game

We study beliefs and choices in a repeated normal-form game. In addition to a baseline treatment with common knowledge of the game structure, feedback about choices in the previous period and random matching, we run treatments (i) with fixed matching, (ii) without information about the opponent’s payoffs, and (iii) without feedback about previous play. Using Stahl and Wilson’s (1995) model of limited strategic reasoning, we classify behavior with regard to its strategic sophistication and consider its development over time. In the treatments with feedback and full information about the game, we observe more strategic play, more best-responses to beliefs and more accurate beliefs over time. While feedback is the main driving force of learning to play strategically and for forming beliefs that accurately predict the behavior of the opponent, both incomplete information about the opponent’s payoffs or lack of feedback lead to a stagnation of best-response rates over time. ZUSAMMENFASSUNG - (Information und Erwartungen in einem wiederholten Normalformspiel) Wir untersuchen die Entwicklung von den Erwartungen über das Verhalten des anderen Spielers und den Entscheidungen in einem wiederholten Normalformspiel. Zusätzlich zum Haupttreatment mit common knowledge über das Spiel, Feedback über das Ergebnis in der vorigen Runde und zufälliger Zuordnung der Spieler, gibt es Kontrolltreatments mit (i) festen paarweisen Zuordnungen der Spieler, (ii) ohne Information über die Auszahlungen des anderen Spielers und (iii) ohne Feedback über das Ergebnis der vorigen Runde. Mit Hilfe von Stahl und Wilsons (1995) Modell begrenzten strategischen Verhaltens klassifizieren wir das Verhalten der Teilnehmer im Hinblick auf die strategische Sophistikation. In den Treatments mit Feedback und vollständiger Information über das Spiel nehmen strategisches Verhalten, beste Antworten auf die eigenen Erwartungen und die Akkuratheit der Erwartungen über die Zeit zu. Während Feedback der Hauptgrund dafür ist, dass die Teilnehmer lernen, sich strategisch zu verhalten und korrekte Erwartungen über das Verhalten des anderen Spielers zu bilden, führen sowohl unvollständige Information über die Auszahlungen des Gegenspielers als auch fehlendes Feedback zu einer Stagnation der Rate der besten Antworten über die Zeit.

Information and Beliefs in a Repeated Normal-Form Game

We study beliefs and choices in a repeated normal-form game. In addition to a baseline treatment with common knowledge of the game structure and feedback about choices in the previous period, we run treatments (i) without feedback about previous play, (ii) with no information about the opponent’s payoffs and (iii) with random matching. Using Stahl and Wilson’s (1995) model of limited strategic reasoning, we classify behavior with regard to its strategic sophistication and consider its development over time. We use belief statements to check for the consistency of subjects’ actions with the stated beliefs as well as for the accuracy of their beliefs (relative to the opponent’s true choice). In the baseline treatment we observe more sophisticated play as well as more accurate beliefs and more best responses to beliefs over time. We isolate feedback as the main driving force of learning to play strategically and to form beliefs that accurately predict the behavior of the opponent.beliefs, experiments, strategic uncertainty, learning

Vertices of Lie Modules

Let Lie(n) be the Lie module of the symmetric group S_n over a field F of characteristic p>0, that is, Lie(n) is the left ideal of FS_n generated by the Dynkin-Specht-Wever element. We study the problem of parametrizing non-projective indecomposable summands of Lie(n), via describing their vertices and sources. Our main result shows that this can be reduced to the case when n is a power of p. When n=9 and p=3, and when n=8 and p=2, we present a precise answer. This suggests a possible parametrization for arbitrary prime powers.Comment: 26 page

Do Legal Standards Affect Ethical Concerns of Consumers? An Experiment on Minimum Wages

To address the impact of regulation on ethical concerns of consumers, we study the example of minimum wages. In our experimental market, consumers have monopsony power, firms set prices and wages, and workers are passive recipients of a wage payment. We find that the consumers exhibit considerable fairness towards the workers by buying from the firm with the higher price and the higher wage. We also find that consumers have a tendency to split their demand equally between firms, which is a simple strategy to provide both workers with a minimal payoff. Introducing a minimum wage in a mature market raises average wages despite its significant crowding-out effects on consumers' fairness concerns. Abolishing a minimum wage crowds in consumers' fairness concerns, but crowding in is not sufficient to avoid overall negative effects on the workers' wages