An introduction to wonderful varieties with many examples of type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mi mathvariant="sans-serif">F</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>

Bravi, Paolo; Morales, Domingo

doi:10.1016/j.jalgebra.2010.01.025

Cited by 30 publications

(12 citation statements)

References 27 publications

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“…In Section 1 we give the definition of spherical system and of other basic notions; for a more accessible introduction see [Lu01,BL09].…”

Section: Introductionmentioning

confidence: 99%

Primitive spherical systems

Bravi

2012

Trans. Amer. Math. Soc.

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A spherical system is a combinatorial object, arising in the theory of wonderful varieties, defined in terms of a root system. All spherical systems can be obtained by means of some general combinatorial procedures (such as parabolic induction and wonderful fiber product) from the so-called primitive spherical systems. Here we classify the primitive spherical systems. As an application, we prove that the quotients of a spherical system are in correspondence with the so-called distinguished subsets of colors

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“…In Section 1 we give the definition of spherical system and of other basic notions; for a more accessible introduction see [Lu01,BL09].…”

Section: Introductionmentioning

confidence: 99%

Primitive spherical systems

Bravi

2012

Trans. Amer. Math. Soc.

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“…(i) It is well known that whenever (see [26, Section 1.4]). It is indeed being part of Luna’s axioms which classify spherical varieties [5, Section 1.2]. Thus, by the definition of , this property holds for all .…”

Section: Root Systems Associated To a Spherical Homogeneous Spacementioning

confidence: 96%

“…Because is obtained from by doubling some particular elements in (see [5, Section 2.4]), it turns out that we also have We denote by the (reduced) root system generated by . Notice that has also Weyl group .…”

Section: Root Systems Associated To a Spherical Homogeneous Spacementioning

confidence: 99%

See 2 more Smart Citations

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 Varieties

Brion¹

2012

Highlights in Lie Algebraic Methods

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An introduction to wonderful varieties with many examples of type F4

Cited by 30 publications

References 27 publications

Primitive spherical systems

Primitive spherical systems

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

Spherical Varieties

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