Abstract
Let G be the special orthogonal group. Let T be a maximal torus in G and B be a Borel subgroup of G containing T. Let λ be a dominant weight with respect to T. Let LΛ denote the line bundle on G/B corresponding to the dominant weight weight λ. We determine bounds and constraints on p for which H0(G/B, Lλ) is irreducible as a G module. We solve the problem in the case when λ = mω1,m > 0, and the cases when λ = 2ω2, 3ω2. For our proof we make use of ideas from standard monomial theory developed by Seshadri and his school.
Dedicated to Prof. C. S. Seshadri on his 70th birthday
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© 2003 Hindustan Book Agency
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Kannan, S.S., Subrahmanyam, K.V. (2003). On representations of special orthogonal groups over fields of positive characteristics. In: Lakshmibai, V., et al. A Tribute to C. S. Seshadri. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-11-8_28
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DOI: https://doi.org/10.1007/978-93-86279-11-8_28
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-39-5
Online ISBN: 978-93-86279-11-8
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