On the little Weyl group of a real spherical space
J.J. Kuit, E. Sayag, Mathematische Annalen 387 (2022) 433–498.
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Journal Article
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Author
Kuit, Job J.;
Sayag, Eitan
Abstract
<jats:title>Abstract</jats:title><jats:p>In the present paper we further the study of the compression cone of a real spherical homogeneous space <jats:inline-formula><jats:alternatives><jats:tex-math>$$Z=G/H$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>Z</mml:mi>
<mml:mo>=</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>H</mml:mi>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula>. In particular we provide a geometric construction of the little Weyl group of <jats:italic>Z</jats:italic> introduced recently by Knop and Krötz. Our technique is based on a fine analysis of limits of conjugates of the subalgebra <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathrm{Lie}(H)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>Lie</mml:mi>
<mml:mo>(</mml:mo>
<mml:mi>H</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> along one-parameter subgroups in the Grassmannian of subspaces of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathrm{Lie}(G)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>Lie</mml:mi>
<mml:mo>(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula>. The little Weyl group is obtained as a finite reflection group generated by the reflections in the walls of the compression cone.</jats:p>
Publishing Year
Journal Title
Mathematische Annalen
Volume
387
Issue
1-2
Page
433-498
LibreCat-ID
Cite this
Kuit JJ, Sayag E. On the little Weyl group of a real spherical space. Mathematische Annalen. 2022;387(1-2):433-498. doi:10.1007/s00208-022-02473-x
Kuit, J. J., & Sayag, E. (2022). On the little Weyl group of a real spherical space. Mathematische Annalen, 387(1–2), 433–498. https://doi.org/10.1007/s00208-022-02473-x
@article{Kuit_Sayag_2022, title={On the little Weyl group of a real spherical space}, volume={387}, DOI={10.1007/s00208-022-02473-x}, number={1–2}, journal={Mathematische Annalen}, publisher={Springer Science and Business Media LLC}, author={Kuit, Job J. and Sayag, Eitan}, year={2022}, pages={433–498} }
Kuit, Job J., and Eitan Sayag. “On the Little Weyl Group of a Real Spherical Space.” Mathematische Annalen 387, no. 1–2 (2022): 433–98. https://doi.org/10.1007/s00208-022-02473-x.
J. J. Kuit and E. Sayag, “On the little Weyl group of a real spherical space,” Mathematische Annalen, vol. 387, no. 1–2, pp. 433–498, 2022, doi: 10.1007/s00208-022-02473-x.
Kuit, Job J., and Eitan Sayag. “On the Little Weyl Group of a Real Spherical Space.” Mathematische Annalen, vol. 387, no. 1–2, Springer Science and Business Media LLC, 2022, pp. 433–98, doi:10.1007/s00208-022-02473-x.
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