A fairly old problem in modular representation theory is to determine the vanishing behavior of the $\mathop {\mathrm Hom}\nolimits $ groups and higher $\mathop {\mathrm Ext}\nolimits $ groups of Weyl modules and to compute the dimension of the $\mathbb{Z} /(p)$-vector space $\mathop {\mathrm Hom}\nolimits _{\bar{A}_r}(\bar{K}_\lambda ,\bar{K}_\mu )$ for any partitions $\lambda $, $\mu $ of $r$, which is the intertwining number. K. Akin, D. A. Buchsbaum, and D. Flores solved this problem in the cases of partitions of length two and three. In this paper, we describe the vanishing behavior of the groups $\mathop {\mathrm Hom}\nolimits _{\bar{A}_r}(\bar{K}_\lambda ,\bar{K}_\mu )$ and provide a new formula for the intertwining number for any $n$-rowed partition.
This study examines the taxation policy of Maria Theresa as evidenced by the situation in Bohemia. A fundamental measure that opened the way for subsequent developments was the passing of the ten-year compact (or "Rezess", as it was known), by the Bohemian parliament in 1748. This law guaranteed a fixed total tax contribution (5,488,155 gulders, 58 crowns) in return for a guarantee that the empress would not demand extra levies, even in the event of war. With the outbreak of the Seven Years’ War, however, the situation changed and in 1756 demands were made for exceptional taxes, military recruits, loans to the state budget, etc. Meanwhile the guarantee of a fixed total tax under the ten-year compact continued to apply. The Treaty of Hubertusburg (1763) brought no relief, as Maria Theresa asked parliament to approve not only an extension of the compact for the following military year, but new exceptional taxes and the reimposition of certain existing indirect taxes. These obligations, together with an increased tax burden in rural communities, remained in place until 1775, when a new ten-year compact was negotiated that lasted until 1789., Jan Lhoták., and Obsahuje bibliografické odkazy