Prime representations from a homological perspective
We explore the relation between self extensions of simple representations of quantum affine algebras and the property of a simple representation being prime. We show that every nontrivial simple representation has a nontrivial self extension. Conversely, we prove that if a simple representation has a unique nontrivial self extension up to isomorphism, then its Drinfeld polynomial is a power of the Drinfeld polynomial of a prime representation. It turns out that, in the sl 2 -case, a simple module is prime if and only if it has a unique nontrivial self extension up to isomorphism. It is tempting to conjecture that this is true in general and we present a large class of prime representations satisfying this homological property
Item Type | Article |
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Keywords | quantum affine algebras, extensions, prime |
Date Deposited | 15 May 2025 12:32 |
Last Modified | 30 May 2025 23:53 |
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picture_as_pdf - 1112.6376v1_.pdf
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subject - Submitted Version