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The cancellations of poles of degenerate Eisenstein series were studied byHanzer and Mui\'{c}. This paper generalizes the method and the result toEisenstein series constructed from inducing two Speh representations$\Delta(\tau,m)|\cdot|^{s_1}\otimes\Delta(\tau,n)|\cdot|^{s_2}$ for the group$GL(m+n,\mathbb{A}_\mathbb{Q})$ for self-dual cuspidal automorphicrepresentation $\tau$ by describing the combinatorics of the relevant Weylgroup coset.

Some Combinatorics in the Cancellation of Poles of Eisenstein Series for $GL(n,\mathbb{A}_\mathbb{Q})$