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

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© 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).

Idioma original	Anglès
Pàgines (de-a)	2933-2961
Revista	Journal of Functional Analysis
Volum	267
DOIs	https://doi.org/10.1016/j.jfa.2014.06.017
Estat de la publicació	Publicada - 1 de gen. 2014

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10.1016/j.jfa.2014.06.017

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

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title = "Classification of invariant valuations on the quaternionic plane",

abstract = "{\textcopyright} 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).",

keywords = "Cosine transform, Hadwiger theorem, K{\"a}hler angle, Valuation",

author = "Andreas Bernig and Gil Solanes",

year = "2014",

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doi = "10.1016/j.jfa.2014.06.017",

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volume = "267",

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journal = "Journal of Functional Analysis",

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T1 - Classification of invariant valuations on the quaternionic plane

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AU - Solanes, Gil

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N2 - © 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).

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

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