arXiv subjects

Daiva Pucinskaite

Publications and source records attributed to Daiva Pucinskaite.

4 recordsLinked to original sources

arXiv2026

Permutations with Verma Multiplicities $[M(p):L(q)] \geq 2$

We consider permutations $q$ in the symmetric group $S_n$ whose Verma multiplicities in the principal block of $\mathcal{O}(\mathfrak{sl}_n)$ satisfy $[M(p):L(q)] \geq 2$. We present a construction along with a diagrammatic visualization, showing how permutations in $S_n$ with this property generate a family of permutations in $S_{n+1}$ that share the same multiplicity property. While the method does not recover all such permutations in $S_{n+1}$, it systematically generates many new examples. In addition, we present all permutations in $S_5$ with $[M(\mathrm{id}):L(q)] \geq 2$ in a Bruhat diagram and describe all permutations in $S_6$ and $S_7$ with non-simple Verma multiplicities.

math.CO↗

arXiv2012

Quasi-hereditary algebras via generator-cogenerators of local self-injective algebras and transfer of Ringel duality

The dominant dimension of algebras in the class A of 1-quasi-hereditary algebras is at least two. By the Morita-Tachikawa Theorem this implies that A is related to a certain class B of algebras via bimodules satisfying the double centralizer condition. In this paper we specify the class B and the modules over algebras in B connected with A. The class A is not closed under taking the Ringel-dual. However the dominant dimension of the Ringel-dual R(q) of a 1-quasi-hereditary algebra q is at least two. This fact induces a corresponding concept of modules over algebras in B which yield the algebras q and R(q) for q in A.

math.RT↗

arXiv2012

1-quasi-hereditary algebras

Motivated by the structure of the algebras associated to the blocks of the BGG-category O we define a subclass of quasi-hereditary algebras called 1-quasi-hereditary. Many properties of these algebras only depend on the defining partial order. In particular, we can determine the quiver and the form of the relations. Moreover, if the Ringel dual of a 1-quasi-hereditary algebra is also 1-quasi-hereditary, then the structure of the characteristic tilting module can be computed.

math.RT↗

arXiv2012

1-quasi-hereditary algebras: Examples and invariant submodules of projectives

In arXiv:1104.4441 it was shown that any 1-quasi-hereditary algebra affords a particular basis which is related to a given partial order on the set of simple modules. We show that the modules generated by these basis-elements are also modules over the endomorphism algebra of some projective indecomposable modules. In case the Ringel-dual of a 1-quasi-hereditary algebra is also 1-quasi-hereditary, we describe all local Delta-good submodules of projective indecomposable modules. We also consider several examples.

math.RT↗