dorsal/arxiv
View SchemaQuantum groups and representations with highest weight
| Authors | Joseph Bernstein, Tanya Khovanova |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9704007 |
| URL | https://arxiv.org/abs/q-alg/9704007 |
Abstract
We consider a special category of Hopf algebras, depending on parameters $\Sigma$ which possess properties similar to the category of representations of simple Lie group with highest weight $\lambda$. We connect quantum groups to minimal objects in this categories---they correspond to irreducible representations in the category of representations with highest weight $\lambda$. Moreover, we want to correspond quantum groups only to finite dimensional irreducible representations. This gives us a condition for $\lambda$: $\lambda$--- is dominant means the minimal object in the category of representations with highest weight $\lambda$ is finite dimensional. We put similar condition for $\Sigma$. We call $\Sigma$ dominant if the minimal object in corresponding category has polynomial growth. Now we propose to define quantum groups starting from dominant parameters $\Sigma$.
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"abstract": "We consider a special category of Hopf algebras, depending on parameters\n$\\Sigma$ which possess properties similar to the category of representations of\nsimple Lie group with highest weight $\\lambda$. We connect quantum groups to\nminimal objects in this categories---they correspond to irreducible\nrepresentations in the category of representations with highest weight\n$\\lambda$. Moreover, we want to correspond quantum groups only to finite\ndimensional irreducible representations. This gives us a condition for\n$\\lambda$: $\\lambda$--- is dominant means the minimal object in the category of\nrepresentations with highest weight $\\lambda$ is finite dimensional. We put\nsimilar condition for $\\Sigma$. We call $\\Sigma$ dominant if the minimal object\nin corresponding category has polynomial growth. Now we propose to define\nquantum groups starting from dominant parameters $\\Sigma$.",
"arxiv_id": "q-alg/9704007",
"authors": [
"Joseph Bernstein",
"Tanya Khovanova"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Quantum groups and representations with highest weight",
"url": "https://arxiv.org/abs/q-alg/9704007"
},
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