Spherical orbit closures in simple projective spaces and their normalizations

Gandini, Jacopo

doi:10.1007/s00031-011-9120-2

Cited by 11 publications

(9 citation statements)

References 18 publications

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“…Restricting to the strongly solvable case, we say that a spherical subgroup H ⊂ G contained in B is wonderful if w 0 X (G/H) = ZΣ, where Σ is the set introduced in Definition 3. 16. The fact that this definition agrees with the general one is a consequence of Proposition 2.3 (see Remark 3.18).…”

Section: 2supporting

confidence: 55%

Orbits of strongly solvable spherical subgroups on the flag variety

Gandini

Pezzini

2017

J Algebr Comb

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Let G be a connected reductive complex algebraic group and B a Borel subgroup of G. We consider a subgroup (Formula presented.) which acts with finitely many orbits on the flag variety G / B, and we classify the H-orbits in G / B in terms of suitable root systems. As well, we study the Weyl group action defined by Knop on the set of H-orbits in G / B, and we give a combinatorial model for this action in terms of weight polytopes

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Section: 2supporting

confidence: 55%

Orbits of strongly solvable spherical subgroups on the flag variety

Gandini

Pezzini

2017

J Algebr Comb

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“…When D is not ample, the variety X D was then studied in [37] in the symmetric case and in [22] in general. More precisely, the orbit structure of X D and that of its normalization X D were analyzed.…”

Section: On the Normality Of Spherical Orbit Closures In Simple Projementioning

confidence: 99%

“…The combinatorics of distinguished subsets of colors allows to describe completely the K-orbits in the closure of O p (see for example [22]), and in particular to prove that O p O p has codimension at least two in O p . Indeed, one sees that this property depends only on the combinatorics of colors and spherical roots, and in this case the combinatorics is the same as that of the complex model orbit, whose boundary has codimension at least two.…”

Section: Proposition 85mentioning

confidence: 99%

Projective normality of model varieties and related results

2016

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Abstract. We prove that the multiplication of sections of globally generated line bundles on a model wonderful variety M of simply connected type is always surjective. This follows by a general argument which works for every wonderful variety and reduces the study of the surjectivity for every couple of globally generated line bundles to a finite number of cases. As a consequence, the cone defined by a complete linear system over M or over a closed G-stable subvariety of M is normal. We apply these results to the study of the normality of the compactifications of model varieties in simple projective spaces and of the closures of the spherical nilpotent orbits. Then we focus on a particular case proving two specific conjectures of Adams, Huang and Vogan on an analogue of the model orbit of the group of type E 8 .

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“…The weight lattices of , , and allow easily to compare K , , and : indeed, the quotient is diagonalizable (see [8, Corollaire 5.2]), and we have inclusions inducing isomorphisms (see, e.g., [12, Lemma 2.4]) …”

Section: Root Systems Associated To a Spherical Homogeneous Spacementioning

confidence: 99%

On the multiplication of spherical functions of reductive spherical pairs of type A

Bravi¹,

Gandini

2021

Can. J. Math.-J. Can. Math.

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Let G be a simple complex algebraic group and let K ⊂ G be a reductive subgroup such that the coordinate ring of G/K is a multiplicity free G-module. We consider the G-algebra structure of C[G/K], and study the decomposition into irreducible summands of the product of irreducible G-submodules in C[G/K]. When the spherical roots of G/K generate a root system of type A we propose a conjectural decomposition rule, which relies on a conjecture of Stanley on the multiplication of Jack symmetric functions. With the exception of one case, we show that the rule holds true whenever the root system generated by the spherical roots of G/K is a direct sum of subsystems of rank one. MSC2020 -Mathematical Sciences Classification System: 14M27 (05E10 20G05).

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Spherical orbit closures in simple projective spaces and their normalizations

Cited by 11 publications

References 18 publications

Orbits of strongly solvable spherical subgroups on the flag variety

Orbits of strongly solvable spherical subgroups on the flag variety

Projective normality of model varieties and related results

On the multiplication of spherical functions of reductive spherical pairs of type A

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