The determinant of the Gram matrix for a Specht module

@inproceedings{James1979TheDO,
  title={The determinant of the Gram matrix for a Specht module},
  author={Gordon James and George E. Murphy},
  year={1979}
}
Let Se denote the Specht module, defined over the integers, corresponding to the partition p of n. Suppose that e, , e2 ,..., e,, is the standard basis of P, and let ( , ) be the bilinear form on Su defined in [l]. We shall evaluate the determinant of the Gram matrix whose (i, j)th entry is (ei , ej), and shall denote this determinant by det p. Our result is strikingly similar to that obtained by Jantzen for the general linear group. The value of this exercise is that it gives a lower bound on… CONTINUE READING

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