TY - JOUR

T1 - Pizzetti formula on the Grassmannian of 2-planes

AU - Eelbode, D.

AU - Homma, Y.

N1 - Funding Information:
This research was supported by the Fund for Scientific Research-Flanders (FWO-Vlaanderen), Project ‘Construction of algebra realisations using Dirac operators’, Grant G.0116.13N. The second author was partially supported by JSPS KAKENHI Grant Number JP19K03480.
Funding Information:
This research was supported by the Fund for Scientific Research-Flanders (FWO-Vlaanderen), Project ?Construction of algebra realisations using Dirac operators?, Grant G.0116.13N. The second author was partially supported by JSPS KAKENHI Grant Number JP19K03480.
Publisher Copyright:
© 2020, Springer Nature B.V.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - This paper is devoted to the role played by the Higgs algebra H3 in the generalisation of classical harmonic analysis from the sphere Sm-1 to the (oriented) Grassmann manifold Gr o(m, 2) of 2-planes. This algebra is identified as the dual partner (in the sense of Howe duality) of the orthogonal group SO (m) acting on functions on the Grassmannian. This is then used to obtain a Pizzetti formula for integration over this manifold. The resulting formulas are finally compared to formulas obtained earlier for the Pizzetti integration over Stiefel manifolds, using an argument involving symmetry reduction.

AB - This paper is devoted to the role played by the Higgs algebra H3 in the generalisation of classical harmonic analysis from the sphere Sm-1 to the (oriented) Grassmann manifold Gr o(m, 2) of 2-planes. This algebra is identified as the dual partner (in the sense of Howe duality) of the orthogonal group SO (m) acting on functions on the Grassmannian. This is then used to obtain a Pizzetti formula for integration over this manifold. The resulting formulas are finally compared to formulas obtained earlier for the Pizzetti integration over Stiefel manifolds, using an argument involving symmetry reduction.

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U2 - 10.1007/s10455-020-09731-8

DO - 10.1007/s10455-020-09731-8

M3 - Article

AN - SCOPUS:85089099694

SN - 0232-704X

VL - 58

SP - 325

EP - 350

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 3

ER -