Invariant rings and representations of symmetric groups
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The center of the Lie group SU(n) is isomorphic to Zn. If d divides n, the quotient SU(n)/Zd is also a Lie group. Such groups are locally isomorphic, and their Weyl groups W(SU(n)/Zd) are the symmetric group n. However, the integral representations of the Weyl groups are not equivalent. Under the mod p reductions, we consider the structure of invariant rings H∗(BTn−1; Fp)W for W = W(SU(n)/Zd). Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non–polynomial cases.
Abstract
The center of the Lie group SU(n) is isomorphic to Zn. If d divides n, the quotient SU(n)/Zd is also a Lie group. Such groups are locally isomorphic, and their Weyl groups W(SU(n)/Zd) are the symmetric group n. However, the integral representations of the Weyl groups are not equivalent. Under the mod p reductions, we consider the structure of invariant rings H∗(BTn−1; Fp)W for W = W(SU(n)/Zd). Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non–polynomial cases.
참고문헌 (8)
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