1,409 research outputs found

    Characterisations of elementary pseudo-caps and good eggs

    Get PDF
    In this note, we use the theory of Desarguesian spreads to investigate good eggs. Thas showed that an egg in PG(4n1,q)\mathrm{PG}(4n-1, q), qq odd, with two good elements is elementary. By a short combinatorial argument, we show that a similar statement holds for large pseudo-caps, in odd and even characteristic. As a corollary, this improves and extends the result of Thas, Thas and Van Maldeghem (2006) where one needs at least 4 good elements of an egg in even characteristic to obtain the same conclusion. We rephrase this corollary to obtain a characterisation of the generalised quadrangle T3(O)T_3(\mathcal{O}) of Tits. Lavrauw (2005) characterises elementary eggs in odd characteristic as those good eggs containing a space that contains at least 5 elements of the egg, but not the good element. We provide an adaptation of this characterisation for weak eggs in odd and even characteristic. As a corollary, we obtain a direct geometric proof for the theorem of Lavrauw

    Highest weight categories arising from Khovanov's diagram algebra II: Koszulity

    Full text link
    This is the second of a series of four articles studying various generalisations of Khovanov's diagram algebra. In this article we develop the general theory of Khovanov's diagrammatically defined "projective functors" in our setting. As an application, we give a direct proof of the fact that the quasi-hereditary covers of generalised Khovanov algebras are Koszul.Comment: Minor changes, extra sections on Kostant modules and rigidity of cell modules adde
    corecore