Classification of invariant valuations on the quaternionic plane

Andreas Bernig; Gil Solanes

doi:10.1016/j.jfa.2014.06.017

Classification of invariant valuations on the quaternionic plane

Andreas Bernig, Gil Solanes

Research output: Contribution to journal › Article › Research › peer-review

18 Citations (Scopus)

Abstract

© 2014 Elsevier Inc. We describe the orbit space of the action of the group Sp(2)Sp(1) on the real Grassmann manifolds Grk(H{double-struck}2) in terms of certain quaternionic matrices of Moore rank not larger than 2. We then give a complete classification of valuations on the quaternionic plane H{double-struck}2 which are invariant under the action of the group Sp(2)Sp(1).

Original language	English
Pages (from-to)	2933-2961
Journal	Journal of Functional Analysis
Volume	267
DOIs	https://doi.org/10.1016/j.jfa.2014.06.017
Publication status	Published - 1 Jan 2014

Keywords

Cosine transform
Hadwiger theorem
Kähler angle
Valuation

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10.1016/j.jfa.2014.06.017

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AU - Solanes, Gil

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AB - © 2014 Elsevier Inc. We describe the orbit space of the action of the group Sp(2)Sp(1) on the real Grassmann manifolds Grk(H{double-struck}2) in terms of certain quaternionic matrices of Moore rank not larger than 2. We then give a complete classification of valuations on the quaternionic plane H{double-struck}2 which are invariant under the action of the group Sp(2)Sp(1).

KW - Cosine transform

KW - Hadwiger theorem

KW - Kähler angle

KW - Valuation

UR - https://www.scopus.com/pages/publications/84908575035

U2 - 10.1016/j.jfa.2014.06.017

DO - 10.1016/j.jfa.2014.06.017

M3 - Article

SN - 0022-1236

VL - 267

SP - 2933

EP - 2961

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

ER -

Classification of invariant valuations on the quaternionic plane

Abstract

Keywords

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