BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Ian Musson (University of Wisconsin Milwaukee)
DTSTART:20211130T170000Z
DTEND:20211130T180000Z
DTSTAMP:20260423T021409Z
UID:ONCAS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ONCAS/10/">H
 ow to construct the lattice of submodules of a multiplicity free module fr
 om partial information</a>\nby Ian Musson (University of Wisconsin Milwauk
 ee) as part of ONCAS Online Noncommutative Algebra Seminar\n\n\nAbstract\n
 In general it is a difficult problem to construct the lattice of submodule
 s $L(M )$ given module $M$. In [Sta12] a method is outlined for constuctin
 g a distributive lattice from a knowledge of its join irreducibles. Howeve
 r it is not an easy task to identify all join irreducible submodules of a 
 given module. In the case of a multiplicity free module M we present an al
 ternative method based on the composition factors. As input we require a s
 et of submodules $A_1\,\\ldots\, A_n$ whose submodule lattice is known\, w
 hich contain all composition factors of $M$\, and for which all intersecti
 ons $A_i \\cap A_j$ are known. From this we can reconstruct $L(M)$. We ill
 ustrate the process for a Verma module M for the Lie superalgebra $\\mathf
 rak{osp}(3\, 2)$. In this case\, $L(M)$ is isomorphic to the (extended) fr
 ee distributive lattice of rank 3. This is well-known\, but quite complica
 ted lattice. Indeed $M$\nhas 20 submodules and 8 composition factors\, eac
 h with multiplicity one.\n\n$\\mathbf{Bibliography}$\n\n[Sta12] R. P. Stan
 ley\, Enumerative combinatorics. Volume 1\, 2nd ed.\, Cambridge Studies in
  Advanced Mathematics\, vol. 49\, Cambridge University Press\, Cambridge\,
  2012. MR2868112\n
LOCATION:https://researchseminars.org/talk/ONCAS/10/
END:VEVENT
END:VCALENDAR