Invariant trilinear forms for spherical degenerate principal series of complex symplectic groups

Clare, Pierre

doi:10.1142/s0129167x15501074

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…some classical complex simple Lie groups G C . See also Example 9.4 for some recent works on integral trilinear forms by Clerc et al[CKØP11,C15] which fits well into the framework of Theorem 4.7.…”

supporting

confidence: 56%

Finite multiplicity theorems for induction and restriction

Kobayashi

Oshima

2013

Advances in Mathematics

135

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We find upper and lower bounds of the multiplicities of irreducible admissible representations $\pi$ of a semisimple Lie group $G$ occurring in the induced representations $Ind_H^G\tau$ from irreducible representations $\tau$ of a closed subgroup $H$. As corollaries, we establish geometric criteria for finiteness of the dimension of $Hom_G(\pi,Ind_H^G \tau)$ (induction) and of $Hom_H(\pi|_H,\tau)$ (restriction) by means of the real flag variety $G/P$, and discover that uniform boundedness property of these multiplicities is independent of real forms and characterized by means of the complex flag variety.Comment: to appear in Advances in Mathematic

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supporting

confidence: 56%

Finite multiplicity theorems for induction and restriction

Kobayashi

Oshima

2013

Advances in Mathematics

135

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“…Hence the dimension of these spaces represent intertwining numbers or decomposition numbers of tensor products. For applications, it is most interesting to consider cases, where these dimensions are finite, which corresponds to rank one situations, see [1][2][3][4][5][6][7][8][9][10][11][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Invariant trilinear forms for SL(3,R)

Deitmar

2018

Preprint

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We give a detailed analysis of the orbit structure of the third power of the flag variety attached to SL 3 (R). It turns out that 36 generalized Schubert cells split into 70 orbits plus one continuous family of orbits. On the latter, we construct invariant distributions and thus give an instance of the existence of infinitely many linearly independent triple products of induced representations. Contents 1 Orbit structure 3 2 Principal series 11

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