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In Smith Normal Form of powers of a matrix someone has commented saying that one can reformulate many questions about Smith normal forms in the language of affine buildings. I wanted to know of a reference for this link or an explanation of how they are related.

Thank you

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This is discussed in:

Shemanske, Thomas R., The arithmetic and combinatorics of buildings for $\text{Sp}_n$., Trans. Am. Math. Soc. 359, No. 7, 3409-3423 (2007). ZBL1126.20019.

(see section 4).

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