Special classes of homomorphisms between generalized Verma modules for ${{\mathscr{U}}}_{q}(su(n,n))$
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- Jakobsen_2019_J._Phys.__Conf._Ser._1194_012055
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We study homomorphisms between quantized generalized Verma modules M(Vλ) φλ,λ1→ M(Vλ1 ) for uq (su(n; n)). There is a natural notion of degree for such maps, and if the map is of degree k, we write φkλ,λ1. We examine when one can have a series of such homomorphisms φ1λn-1,λ n φ1λn-1,λ n ⋯ o φ1λ, λ1 = Detq, where Detq denotes the map M(Vλ)ϵ p → detq p ϵ 2 M(Vλn). If, classically, su(n; n)C = p ⊗(su(n) ⊗su(n) ⊗C) ⊗p+, then λ = (λL, λR,λ) and λn = (λL;λRλ+2). The answer is then that - must be one-sided in the sense that either λL = 0 or λR = 0 (non-exclusively). There are further demands on λ if we insist on Uq(gC) homomorphisms. However, it is also interesting to loosen this to considering only Uq (gC) homomorphisms, in which case the conditions on λ disappear. By duality, there result have implications on covariant quantized difierential operators. We finish by giving an explicit, though sketched, determination of the full set of Uq(gC) homomorphisms φ1λ, λ1. © 2019 Published under licence by IOP Publishing Ltd.
Original language | English |
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Article number | 012055 |
Book series | Journal of Physics: Conference Series |
Volume | 1194 |
Issue number | 1 |
Number of pages | 10 |
ISSN | 1742-6588 |
DOIs | |
Publication status | Published - 2019 |
Event | 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 - Prague, Czech Republic Duration: 9 Jul 2019 → 13 Jul 2019 |
Conference
Conference | 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 |
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Country | Czech Republic |
City | Prague |
Period | 09/07/2019 → 13/07/2019 |
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