The Lattice Structure of Connection Preserving Deformations for q-Painlev\'e Equations I

We wish to explore a link between the Lax integrability of the $q$-Painlev\'e equations and the symmetries of the $q$-Painlev\'e equations. We shall demonstrate that the connection preserving deformations that give rise to the $q$-Painlev\'e equations may be thought of as elements of the groups of Schlesinger transformations of their associated linear problems. These groups admit a very natural lattice structure. Each Schlesinger transformation induces a B\"acklund transformation of the $q$-Painlev\'e equation. Each translational B\"acklund transformation may be lifted to the level of the associated linear problem, effectively showing that each translational B\"acklund transformation admits a Lax pair. We will demonstrate this framework for the $q$-Painlev\'e equations up to and including $q$-$\mathrm{P}_{\mathrm{VI}}$

Corrigendum to "On injective modules and support varieties for the small quantum group"

The proof of Theorem 5.12 in [C.M. Drupieski, On injective modules and support varieties for the small quantum group, Int. Math. Res. Not. 2011 (2011), 2263-2294] does not make sense as written because the algebra $u_\zeta(\mathfrak{b}_\alpha^+)$ need not be a Hopf subalgebra of $u_\zeta(\mathfrak{b}^+)$ unless $\alpha$ is a simple root. This note describes how the proof should be modified to work around this fact.Comment: 2 pages; Corrigendum to [C.M. Drupieski, On injective modules and support varieties for the small quantum group, Int. Math. Res. Not. 2011 (2011), 2263-2294

MS-076: George C. Wynkoop, 2nd Brigade, 2nd Division, Dept. of Pennsylvania

This collection consists of records from George Wynkoop’s service as a Brigadier General in the three month Pennsylvania Volunteers. Over three hundred pieces of correspondence, orders, forms, and daily reports make up the collection. The correspondence and reports come from a variety of locals at which the Department of Pennsylvania set up camp. Locations include Camp Scott and Camp Chambers, Pennsylvania, Hagerstown, Maryland and Harper’s Ferry, Virginia (Today West Virginia). Special Collections and College Archives Finding Aids are discovery tools used to describe and provide access to our holdings. Finding aids include historical and biographical information about each collection in addition to inventories of their content. More information about our collections can be found on our website http://www.gettysburg.edu/special_collections/collections/.https://cupola.gettysburg.edu/findingaidsall/1070/thumbnail.jp

MS-075: Henry W. Siebert, Company E, 16th Pennsylvania Volunteer Cavalry

The Henry W. Siebert journals, of which there are two, cover the years 1863 and 1865 respectively. The journals themselves are leather bound notebooks closed with straps, the whole measuring 3 inches by 6 inches. The 1863 volume numbers 90 pages, with entries for every day. The 1865 diary numbers 150 pages and has entries for January 1, 1865 through May 24, 1865. The entries are generally short in nature, not exceeding a paragraph in length. The text is normally limited to a discussion of the morning weather, general activity of the day and the geographic location reached by nightfall. A number of battles are mentioned, including Chancellorsville, Aldie, Upperville, Gettysburg, Petersburg and Appomattox. Special Collections and College Archives Finding Aids are discovery tools used to describe and provide access to our holdings. Finding aids include historical and biographical information about each collection in addition to inventories of their content. More information about our collections can be found on our website http://www.gettysburg.edu/special_collections/collections/.https://cupola.gettysburg.edu/findingaidsall/1069/thumbnail.jp