arXiv subjects

Fernanda Pereira

Publications and source records attributed to Fernanda Pereira.

5 recordsLinked to original sources

arXiv2026

Counting, Symmetries and Equivalence Classes of Sudoku Grids

Sudoku is a widely popular puzzle whose complete grids have been enumerated computationally: there are approximately $6.67 \times 10^{21}$ of them and, up to symmetry and renaming of digits, $5,472,730,538$ essentially different ones. The classical enumeration reduces the count to $44$ equivalence classes of the first band through a chain of ad hoc reductions, leaving the number $44$ without any apparent structural explanation. We present an alternative derivation of these $44$ classes, in which they arise as isomorphism classes of unordered triples (multisets) of column partitions under relabeling, a single invariant that replaces the original chain of reductions. This invariant makes it possible to apply Burnside's Lemma by hand: we recover $44$ through a closed derivation requiring no computational enumeration.

math.GM↗

arXiv2018

Non-Minimality of Certain Irregular Coherent Preminimal Affinizations

Let $\mathfrak g$ be a finite-dimensional simple Lie algebra of type $D$ or $E$ and $λ$ be a dominant integral weight whose support bounds the subdiagram of type $D_4$. We study certain quantum affinizations of the simple $\mathfrak g$-module of highest weight $λ$ which we term preminimal affinizations of order two (this is the maximal order for such $λ$). This class can be split in two: the coherent and the incoherent affinizations. If $λ$ is regular, Chari and Pressley proved that the associated minimal affinizations belong to one of the three equivalent classes of coherent preminimal affinizations. In this paper we show that, if $λ$ is irregular, the coherent preminimal affinizations are not minimal under certain hypotheses. Since these hypotheses are always satisfied if $\mathfrak g$ is of type $D_4$, this completes the classification of minimal affinizations for type $D_4$ by giving a negative answer to a conjecture of Chari-Pressley stating that the coherent and the incoherent affinizations were equivalent in type $D_4$ (this corrects the opposite claim made by the first author in a previous publication).

math.RT↗

arXiv2017

On Tensor Products of a Minimal Affinization with an Extreme Kirillov-Reshetikhin Module for type A

For a quantum affine algebra of type A, we describe the composition series of the tensor product of a general minimal affinization with a Kirillov-Resehtikhin module associated to an extreme node of the Dynkin diagram of the underlying simple Lie algebra.

math.RT↗

arXiv2015

Graded limits of simple tensor product of Kirillov-Reshetikhin modules for $U_q(\tilde{\mathfrak {sl}}_{n+1})$

We study the graded limits of simple $U_q(\tilde{\mathfrak{sl}}_{n+1})$-modules which are isomorphic to tensor products of Kirillov-Reshetikhin modules associated to a fix fundamental weight. We prove that every such module admits a graded limit which is isomorphic to the fusion product of the graded limits of its tensor factors. Moreover, using recent results of Naoi, we exhibit a set of defining relations for these graded limits.

math.QA↗

arXiv2010

Graded limits of minimal affinizations and Beyond: the multiplicty free case for type E6

We obtain a graded character formula for certain graded modules for the current algebra over a simple Lie algebra of type E6. For certain values of their highest weight, these modules were conjectured to be isomorphic to the classical limit of the corresponding minimal affinizations of the associated quantum group. We prove that this is the case under further restrictions on the highest weight. Under another set of conditions on the highest weight, Chari and Greenstein have recently proved that they are projective objects of a full subcategory of the category of graded modules for the current algebra. Our formula applies to all of these projective modules.

math.RT↗