Unity of the four species
arba minim · achdus · sukkah · Klal Yisrael · Shabbos
הד' מינים הם לאגוד ולחבר נפשות בנ"י.
The four species (arba'ah minim) serve to bind and join together the souls of Bnei Yisrael.
The deeper purpose of taking the lulav and its companions is achdus (unity) — bundling together the different "types" within Klal Yisrael into one.
כמ"ש במד' יש בהם שיש להם טעם וריח כו'.
As the Midrash says: among them are some that have taste and some that have fragrance, etc.
The Midrash explains that the four species correspond to four kinds of Jews — some with Torah ("taste"), some with mitzvos ("fragrance") — and the mitzvah is precisely to bind them all together.
ועל ידי האגודה זוכין לכנוס לסוכה דכתיב אהבת כלולותיך לכתך אחרי כו'.
And through this binding together they merit to enter the sukkah, as it is written: "the love of your bridal days, your following after Me..." (Yirmiyahu 2:2).
Only once Bnei Yisrael are unified can they enter the embrace of the sukkah — the same love with which they followed Hashem into the wilderness "as a bride."
שאין יכולין לבוא להמשכה זו להיות נמשך אחר הבורא ית'.
For they cannot come to this drawing-after — to be drawn after the Creator, may He be blessed —
The ability to be drawn after Hashem, following Him into the unknown, is not available to the isolated individual.
רק ע"י שמכניסין עצמן בכלל ישראל.
except by bringing themselves into the klal (collective) of Yisrael.
A person can attain that closeness only by nullifying himself into the whole of Klal Yisrael and becoming part of the collective.
ודרשו חכמים כל האזרח כו' כל ישראל ראוין לישב בסוכה אחת.
And Chazal expounded: "every native-born (kol ha'ezrach)..." — all of Yisrael are fit to sit in a single sukkah.
The Gemara learns from "kol ha'ezrach" that in principle all of Bnei Yisrael could dwell in one sukkah — an expression of how the sukkah unites them as one.
וכל הראוי לבילה אין בילה מעכבת.
And whatever is fit for mixing — the mixing does not hold it back.
Just as in offerings, once something is fit to be blended the actual blending is not indispensable — so too the potential for unity already does its work, even before it is fully realized.
לכן בשבת אין צריכין לולב.
Therefore on Shabbos one does not need the lulav.
The lulav's whole task is to create unity; on Shabbos that unity is already present, so the lulav is not required.
כי בשבת מתאחד ג"כ נפשות בנ"י כמ"ש דמתאחדין ברזא דאחד:
For on Shabbos the souls of Bnei Yisrael also become unified, as it is said that they "become one in the secret of the One."
Shabbos itself draws all the souls of Bnei Yisrael into oneness, bound up in the mystery of Hashem's absolute unity — accomplishing intrinsically what the lulav accomplishes on the other days.
Summary: The mitzvah of the four species is to bind together the differing types within Bnei Yisrael into one, and only through that achdus can a person enter the sukkah and be drawn after Hashem with bridal love. Since a Jew reaches this closeness only by joining the klal, and since Shabbos already unifies all souls "in the secret of the One," the unifying lulav is not needed on Shabbos.