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typo fixed
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Dima Pasechnik
Dima Pasechnik
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Assuming $S^2=I$, your other two relations give you a presentation for the symmetric group of orderdegree 3. So you want to find linear representations of this group (satisfying the extra condition $B=DJ$). In particular, note that $B$ and $S$ have the same eigenvalues. Also, note that the number of -1's in $S$ gives you a constraint on the irreducible subconstituents of your representation.

Assuming $S^2=I$, your other two relations give you a presentation for the symmetric group of order 3. So you want to find linear representations of this group (satisfying the extra condition $B=DJ$). In particular, note that $B$ and $S$ have the same eigenvalues. Also, note that the number of -1's in $S$ gives you a constraint on the irreducible subconstituents of your representation.

Assuming $S^2=I$, your other two relations give you a presentation for the symmetric group of degree 3. So you want to find linear representations of this group (satisfying the extra condition $B=DJ$). In particular, note that $B$ and $S$ have the same eigenvalues. Also, note that the number of -1's in $S$ gives you a constraint on the irreducible subconstituents of your representation.

Source Link
Dima Pasechnik
Dima Pasechnik
  • 14k
  • 2
  • 34
  • 70

Assuming $S^2=I$, your other two relations give you a presentation for the symmetric group of order 3. So you want to find linear representations of this group (satisfying the extra condition $B=DJ$). In particular, note that $B$ and $S$ have the same eigenvalues. Also, note that the number of -1's in $S$ gives you a constraint on the irreducible subconstituents of your representation.