A066051 Maximal degree of an irreducible representation of the group of n X n signed permutation matrices.

1, 2, 3, 8, 20, 80, 210, 672, 2688, 10080, 44352, 236544, 960960, 4324320, 20270250, 104247000, 522762240, 3024552960, 15713497800, 108973522944, 625746401280, 3824005785600, 24049411386000, 160329409240000, 858907549500000, 5226869622374400

Offset: 1

Author

Sharon Sela (sharonsela(AT)hotmail.com), Dec 29 2001

Keywords

• nonn
• nice

Comments

This group is also the automorphism group of the n-dimensional hypercube and the wreath product of the cyclic group C_2 and the symmetric group S_n.

The number of irreducible representations is given in A000712; the order of the group in A000165.

The group is also the Weyl group of type B_n. - Eric M. Schmidt, Sep 21 2013

References

• Roger W. Carter, Finite Groups of Lie Type: Conjugacy Classes And Complex Characters. Wiley, 1985.

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..40

Crossrefs

Cf. A000712, A000165, A003040.

Programs

GAP

to produce a(8): c := CyclicGroup(2); s := SymmetricGroup(8); w := WreathProduct(c,s); Display(CharacterTable(w));

Sage

def A066051(n) : return factorial(n) // min(prod(A.hooks()) * prod(B.hooks()) for (A,B) in PartitionTuples(2,n)) # Eric M. Schmidt, Sep 21 2013

Extensions

More terms from Eric M. Schmidt, Sep 21 2013