Specht modules labelled by hook bipartitions II

We continue the study of Specht modules labelled by hook bipartitions for the Iwahori--Hecke algebra of type $B$ with $e\in\{3,4,\dots\}$ via the cyclotomic Khovanov--Lauda--Rouquier algebra $\mathscr{H}_n^{\Lambda}$. Over an arbitrary field, we explicitly determine the graded decomposition submatrices for $\mathscr{H}_n^{\Lambda}$ comprising rows corresponding to hook bipartitions.Comment: 54 pages, comments are welcome; v2 extends the introduction and significantly shortens the pape

Decomposable Specht modules indexed by bihooks

We study the decomposability of Specht modules labelled by bihooks, bipartitions with a hook in each component, for the Iwahori--Hecke algebra of type $B$. In all characteristics, we determine a large family of decomposable Specht modules, and conjecture that these provide a complete list of decomposable Specht modules indexed by bihooks. We prove the conjecture for small $n$.Comment: 46 pages. Final version to appear in Pacific Journal of Mathematic

La recherche partenariale : le modèle de l’ARUC-ÉS et du RQRP-ÉS

Ce document vise à faire connaître l’expérience de l’Alliance et du Réseau auprès de tous ceux qui s’intéressent aux pratiques de recherche en partenariat et à promouvoir la recherche universitaire au service des milieux de pratique.L’Alliance de recherche universités-communautés en économie sociale et le Réseau québécois de recherche partenariale en économie sociale sont reconnaissants de l’aide financière qu’ils reçoivent du Conseil de recherche en sciences humaines du Canada et de l’Université du Québec à Montréal

Decomposable Specht modules indexed by bihooks II

Previously, the last two authors found large families of decomposable Specht modules labelled by bihooks, over the Iwahori--Hecke algebra of type $B$. In most cases we conjectured that these were the only decomposable Specht modules labelled by bihooks, proving it in some instances. Inspired by a recent semisimplicity result of Bowman, Bessenrodt and the third author, we look back at our decomposable Specht modules and show that they are often either semisimple, or very close to being so. We obtain their exact structure and composition factors in these cases. In the process, we determine the graded decomposition numbers for almost all of the decomposable Specht modules indexed by bihooks.Comment: 33 pages, comments are welcome. v2 is the final version, to appear in Algebras and Representation Theor

Crianças surdas, humor e política educacional

Deaf children need true inclusion to learn, entailing consistent, pervasive use of visual-learning techniques (Hauser et al. 2010). This is achieved via bilingual education policies that permit teachers to engage in deaf pedagogy using sign language (Quadros and Stumpf in press and Quadros 2018).  Educational policies advocating inclusion via an interpreter in the mainstreamed classroom create the “illusion of inclusion” (Glickman 2003).  We argue that, in either case, humor can aid inclusion. Understanding humor is a developmental ability, related to cognitive, social, linguistic, and metalinguistic competence. Additionally, learning how humor is understood and expressed contributes to language mastery (Huss 2008; Garner 2006). However, we find little discussion of humor in deaf education (but see Sanders 1986; Luckner and Yarger 1997; and Ashton et al. 2012). We contend that deaf students have the right to learn through humor and play, throughout school.  Educational policies should reflect that. Educators understand that games are important for learning at any age, and especially for the very young where play is learning, and learning is play. We offer examples of how to modify common classroom activities to extend their effectiveness to deaf children and enhance their effectiveness with hearing children, from dance making mathematical concepts visually apparent, through sign language play encouraging creativity, to mime and theatre techniques illustrating geological facts.Los niños sordos necesitan una verdadera inclusión para aprender, por un uso consistente y generalizado de las técnicas de aprendizaje visual. Esto se hace a través de políticas de educación bilingüe que permiten a los profesores involucrarse en pedagogía sorda usando lenguaje de signos. Las políticas educativas que defienden la inclusión a través de un intérprete en el aula integrada crean la "ilusión de inclusión". Defendemos que, en ambos casos, el humor puede ayudar en la inclusión. La comprensión del humor es una habilidad de desarrollo, relacionada con la competencia cognitiva, social, lingüística y metalinguística. Además, aprender cómo comprender y producir el humor contribuye al dominio de la lengua. Sin embargo, encontramos poca discusión sobre el humor en la educación de sordos. Nosotros afirmamos que los alumnos sordos tienen el derecho de aprender a través del humor y la broma en la escuela. Las políticas educativas deben reflejar esto. Los educadores entienden que los juegos son importantes para el aprendizaje a cualquier edad y, especialmente, para los más jóvenes, donde jugar es aprender, y aprender es broma. Ofrecemos ejemplos de cómo modificar las actividades en el aula para aumentar la eficacia con los niños sordos y oyentes, de la danza haciendo los conceptos matemáticos visualmente aparentes, usando la lengua de signos creativa, y técnicas de mímica y teatro para enseñar hechos geológicos.As crianças surdas precisam de uma verdadeira inclusão para aprender, por um uso consistente das técnicas de aprendizagem visual. Isto é feito através de políticas de educação bilíngue com direitos linguísticos para usar a língua de sinais que permitem aos professores se engajar em pedagogia surda usando língua de sinais. Políticas educacionais que defendem a inclusão por meio de um intérprete na sala de aula integrada criam a “ilusão de inclusão”. Defendemos que, em ambos os casos, o humor pode ajudar na inclusão. A compreensão do humor é uma habilidade de desenvolvimento, relacionada à competência cognitiva, social, linguística e metalinguística. Além disso, aprender como compreender e produzir o humor contribui para o domínio da língua. No entanto, encontramos pouca discussão sobre humor na educação de surdos. Nós afirmamos que os alunos surdos têm o direito de aprender através do humor e da brincadeira na escola. Políticas educacionais e de direitos linguísticos devem refletir isso. Os educadores entendem que os jogos são importantes para a aprendizagem em qualquer idade e, especialmente, para os mais novos, onde brincar é aprendizagem, e aprender é brincadeira. Oferecemos exemplos de como modificar as atividades em sala de aula para aumentar a eficácia com as crianças surdas e ouvintes, da dança tornando os conceitos matemáticos visualmente aparentes, usando a língua de sinais criativa, e técnicas de mímica e teatro para ensinar fatos geológicos

Report from the International Clinical Librarian Conference, University of Edinburgh, 10-12 June 2015, Edinburgh

The EAHIL Workshop provided an opportunity for the International Clinical Librarian Conference (ICLC) to run a satellite conference before the official opening of the Workshop. ICLC aim to hold bi-annual conferences either stand alone, or in collaboration with another meeting. Aimed at those with an interest in clinical or outreach librarianship the 2015 ICLC welcomed a range of presentations on this field of the work

Graded representations of Khovanov-Lauda-Rouquier algebras

PhDThe Khovanov{Lauda{Rouquier algebras Rn are a relatively new family of Z-graded algebras. Their cyclotomic quotients R n are intimately connected to a smaller family of algebras, the cyclotomic Hecke algebras H n of type A, via Brundan and Kleshchev's Graded Isomorphism Theorem. The study of representation theory of H n is well developed, partly inspired by the remaining open questions about the modular representations of the symmetric group Sn. There is a profound interplay between the representations for Sn and combinatorics, whereby each irreducible representation in characteristic zero can be realised as a Specht module whose basis is constructed from combinatorial objects. For R n , we can similarly construct their representations as analogous Specht modules in a combinatorial fashion. Many results can be lifted through the Graded Isomorphism Theorem from the symmetric group algebras, and more so from H n , to the cyclotomic Khovanov{Lauda{Rouquier algebras, providing a foundation for the representation theory of R n . Following the introduction of R n , Brundan, Kleshchev and Wang discovered that Specht modules over R n have Z-graded bases, giving rise to the study of graded Specht modules. In this thesis we solely study graded Specht modules and their irreducible quotients for R n . One of the main problems in graded representation theory of R n , the Graded Decomposition Number Problem, is to determine the graded multiplicities of graded irreducible R n -modules arising as graded composition factors of graded Specht modules. We rst consider R n in level one, which is isomorphic to the Iwahori{Hecke algebra of type A, and research graded Specht modules labelled by hook partitions in this context. In quantum characteristic two, we extend to R n a result of Murphy for the symmetric groups, determining graded ltrations of Specht modules labelled by hook partitions, whose factors appear as Specht modules labelled by two-part partitions. In quantum characteristic at least three, we determine an analogous R n -version of Peel's Theorem for the symmetric groups, providing an alternative approach to Chuang, Miyachi and Tan. We then study graded Specht modules labelled by hook bipartitions for R n in level two, which is isomorphic to the Iwahori{Hecke algebra of type B. In quantum characterisitic at least three, we completely determine the composition factors of Specht modules labelled by hook bipartitions for R n , together with their graded analogues.Engineering and Physical Sciences Research Council, Queen Mary University of London

SL2 tilting modules in the mixed case

Using the non-semisimple Temperley-Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for $\mathrm{SL}_{2}$ in the mixed case. This simultaneously generalizes the semisimple situation, the case of the complex quantum group at a root of unity, and the algebraic group case in positive characteristic. We describe character formulas and give a presentation of the category of tilting modules as an additive category via a quiver with relations. Turning to the monoidal structure, we describe fusion rules and obtain an explicit recursive description of the appropriate analog of Jones-Wenzl projectors. We also discuss certain theta values, the tensor ideals, mixed Verlinde quotients and the non-degeneracy of the braiding.Comment: 53 pages, many figures, comments welcom