Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups $O(p,q)$

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Toshiyuki Kobayashi¹  Alex Leontiev¹ 

[1] Graduate School of Mathematical Sciences, The University of Tokyo;Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo

关键词: Symmetric polynomials;    Grothendieck polynomials;    K-theory;    Grassmannians;    Schubert varieties.;   

DOI  :  10.3792/pjaa.93.86

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

For the pair $(G, G') =(O(p+1, q+1), O(p,q+1))$, we construct and give a complete classification of intertwining operators ( symmetry breaking operators ) between most degenerate spherical principal series representations of $G$ and those of the subgroup $G'$, extending the work initiated by Kobayashi and Speh [Mem. Amer. Math. Soc. 2015] in the real rank one case where $q=0$. Functional identities and residue formulæ of the regular symmetry breaking operators are also provided explicitly. The results contribute to Program C of branching problems suggested by the first author [Progr. Math. 2015].

【 授权许可】

Unknown