Fabrizio Caselli
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View article: Embeddings of E(1,6) in E(5,10) and E(4,4)
Embeddings of E(1,6) in E(5,10) and E(4,4) Open
We study the embeddings of the exceptional infinite-dimensional Lie superalgebra E(1,6) in the exceptional Lie superalgebras E(5,10) and E(4,4). These questions arose in the recent works on enhanced symmetries in some supersymmetric theori…
View article: A Lie conformal superalgebra and duality of representations for E(4,4)
A Lie conformal superalgebra and duality of representations for E(4,4) Open
We construct a duality functor in the category of continuous representations of the Lie superalgebra E(4,4), the only exceptional simple linearly compact Lie superalgebra, for which it wasn't known. This is achieved by constructing a Lie c…
View article: Classification of finite irreducible conformal modules for K4′
Classification of finite irreducible conformal modules for K4′ Open
We classify finite irreducible modules over the conformal superalgebra K4′ by their correspondence with finite conformal modules over the associated annihilation superalgebra A(K4′). This is achieved by a complete classification of singula…
View article: Classification of finite irreducible conformal modules for $K'_4$
Classification of finite irreducible conformal modules for $K'_4$ Open
We classify the finite irreducible modules over the conformal superalgebra $K'_{4}$ by their correspondence with finite conformal modules over the associated annihilation superalgebra $\mathcal A(K'_{4})$. This is achieved by a complete cl…
View article: Weak generalized lifting property, Bruhat intervals, and Coxeter matroids
Weak generalized lifting property, Bruhat intervals, and Coxeter matroids Open
We provide a weaker version of the generalized lifting property that holds in complete generality for all Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also de…
View article: Pircon kernels and up-down symmetry
Pircon kernels and up-down symmetry Open
We show that a symmetry property that we call the up-down symmetry implies that the Kazhdan--Lusztig $R^x$-polynomials of a pircon $P$ are a $P$-kernel, and we show that this property holds in the classical cases. Then, we enhance and exte…
View article: Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids
Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids Open
We provide a weaker version of the generalized lifting property that holds in complete generality for all Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also de…
View article: Low Degree Morphisms of E(5, 10)-Generalized Verma Modules
Low Degree Morphisms of E(5, 10)-Generalized Verma Modules Open
In this paper we face the study of the representations of the exceptional Lie superalgebra E(5,10). We recall the construction of generalized Verma modules and give a combinatorial description of the restriction to sl5 of the Verma module …
View article: The generalized lifting property of Bruhat intervlas
The generalized lifting property of Bruhat intervlas Open
In [E. Tsukerman and L. Williams, {\em Bruhat Interval Polytopes}, Advances in Mathematics, 285 (2015), 766-810] it is shown that every Bruhat interval of the symmetric group satisfies the so-called generalized lifting property. In this pa…