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Multiplicities for tensor products on Special linear versus Classical groups
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- In this paper, using computations done through the LiE software, we compare the tensor product of irreducible selfdual representations of the special linear group with those of classical groups to formulate some conjectures relating the two. In the process a few other phenomenon present themselves which we record as questions. More precisely, under the natural correspondence of irreducible finite dimensional selfdual representations of ${\rm SL}_{2n}({\mathbb C})$ with those of ${\rm Spin}_{2n+1}({\mathbb C})$, it is easy to see that if the tensor product of three irreducible representations of ${\rm Spin}_{2n+1}({\rm C})$ contains the trivial representation, then so does the tensor product of the corresponding representations of ${\rm SL}_{2n}({\rm C})$. The paper formulates a conjecture in the reverse direction. We also deal with the pair $({\rm SL}_{2n+1}({\rm C}), {\rm Sp}_{2n}({\rm C}))$.<br />Comment: Revised version!
- Subjects :
- Classical group
20G05
General Mathematics
010102 general mathematics
Special linear group
Algebraic geometry
01 natural sciences
Combinatorics
Number theory
Tensor product
Irreducible representation
0103 physical sciences
Trivial representation
Bijection
FOS: Mathematics
010307 mathematical physics
0101 mathematics
Representation Theory (math.RT)
Mathematics - Representation Theory
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....2527c6cb6c104eb13737bfe50ec8b5f7
- Full Text :
- https://doi.org/10.48550/arxiv.2003.04556