3 research outputs found
On the zero forcing number of the complement of graphs with forbidden subgraphs
Motivated in part by an observation that the zero forcing number for the
complement of a tree on vertices is either or in one
exceptional case, we consider the zero forcing number for the complement of
more general graphs under some conditions, particularly those that do not
contain complete bipartite subgraphs. We also move well beyond trees and
completely study all of the possible zero forcing numbers for the complements
of unicyclic graphs and cactus graphs.Comment: 17 pages, 8 figure
Isomorphism of Modules for Type Dn
In this paper, for the current algebra associated with the Lie algebra \lie{so}_{2n}(\mathbb{C}), we connect particular CV-modules, indexed by pairs of integral weights that satisfy particular conditions, with generalized Demazure modules which were introduced by [Naoi]. In particular, we show an isomorphism of a CV-module and the module generated by the tensor product of generating vectors , for the local Weyl modules W_{\loc}(\lambda) and W_{\loc}(\mu) respectively, i.e. V(\xi(\lambda,\mu))\cong \langle v_\lambda \otimes v_\mu\rangle \subset W_{\loc}(\lambda) \otimes W_{\loc}(\mu). To complete this proof, we construct short exact sequences of CV-modules. Moreover, through this construction, we obtain a Demazure character formula for the CV-module